Almost all of the Nicene-Constantinopolitan Creed was meant to establish the tenets of the Catholic Church, which inherently defined heresy as "anything that contradicts this". However, much of the Creed was actually written with specific heresies in mind.

I believe in one God,
the Father almighty,
maker of heaven and earth,
of all things visible and invisible.

This i meant to be a refutation of Gnostic teachings, which varied, but generally had the central belief that God wasn't simply 'God' (e.g., He was actually an angel, Lucifer is His dualistic opponent). Since the idea of God being the sole deity and creator of the universe is one of the central tenets of almost every branch of Christianity, this was of utmost importance to include.

I believe in one Lord Jesus Christ,
the Only Begotten Son of God,
born of the Father before all ages.
God from God, Light from Light,
true God from true God,
begotten, not made, consubstantial with the Father;
through him all things were made.

This part is also meant to refute Gnosticism (saying Jesus is the son of God) as well as the heresy of Arianism. Arianism believes that Jesus came into existence after God and was therefore God's inferior. The debate between Arianism and the rest of Christianity eventually led to Emperor Constantine convening the Council of Nicea in 325 AD, which was when the Nicene Creed was first formulated.

For us men and for our salvation
He came down from heaven,
and by the Holy Spirit was incarnate of the Virgin Mary,
and became man.

This is once again a refutation of Gnosticism by saying that Jesus was still the son of God made incarnate in human form. Likewise , this verse also deals with the issues of Jesus' humanity/divinity and Mary's role in the matter, which was addressed in the Councils of Ephesus and Chalcedon. By claiming that God the Son was equal to God the Father, and then claiming that He "became man", Jesus had both fully human and fully divine nature, which addresses the heresy of monophysitism (which believed Jesus only had divine nature). As a result, the Virgin Mary was able to be called theotokos, which means 'Mother of God'.

I believe in the Holy Spirit, the Lord, the giver of life,
who proceeds from the Father and the Son,
who with the Father and the Son is adored and glorified,
who has spoken through the prophets.

This verse emphasizes the Holy Spirit and its value in the Trinity, and was the source of God's divine inspiration to mankind through the Prophets of the Old Testament and the transcription of the Gospels. The bolded part (emphasis mine) is known as the filioque clause, which was a source of tension between Latin and Greek rite scholars before the Great Schism. It wasn't in the original creed, but was added in in 583 in the Council of Toledo (which had far more Latin than Greek bishops). Latin scholars argued that Christ said "I will send him [the Holy Spirit] unto you" (John 16:7) in the Gospels, while Greek scholars claimed that it is impossible for the Spirit to be begotten from the Son, since all things can only be begotten from the Father. After the Schism in 1054, the Filioque clause was officially added into the Creed by the Catholic Church.

Source- People of God: The History of Catholic Christianity, by Anthony E. Gilles

Source for the text of the Creed (US Conference of Catholic Bishops)

The Creed you are referring to, known commonly as the Nicene creed, but more technically as the Niceno-Constantinopolitan Creed, is in fact the product of the council of Constantinople (381), not of Nicaea (325), which produced a different creed. It’s often thought that the C Creed is revision of N creed, but an authority as eminent as JND Kelly thinks this is incorrect, and I’m willing to go with him on that point. In actual point of fact, we don’t have a copy of the C creed from the proceedings of 381, but from the Council of Ephesus 451. Nonetheless, the reigning consensus is that the C creed was indeed produced at Constantinople in 381.

It’s important to understand both the background of this Creed, and of creed-making in the 4th century in general. The advent of Arius, a presbyter from Alexandria with radically subordinationist ideas about the Son, coupled with the consolidation of imperial power into the hands of Constantine I, led to the first ‘ecumenical’ council, Nicaea in 325, which effectively shut down Arius and his views. That first creed, and especially the anathema pronouncements attached to it, was specifically designed to exclude Arian theology

Nonetheless, the aftermath of that council revealed some relatively large theological differences in the rest of the church (at least within the Empire, and more specifically the Greek-speaking Eastern half), about how to relate, on a theological and philosophical level, the Father and the Son within the Trinity. Those debates, and associated church-political manoeuvrings, persisted right through until 380/381. At that point, the accession of Theodosius I with his ‘Nicene’ view, the promulgation of a decree called Cunctos Populos, which defined Nicene orthodoxy as the imperial version of Christianity, in agreement with the bishops of Rome and Alexandria, and the council of Constantinople, put to bed most of the other forms of heterodoxy at that time.

So, with that preamble, let’s turn to the text of the creed. Although it does contain some anti-Gnostic elements, that’s not it’s primary concern. Gnosticism was no longer a functional rival for most Christians, and the real ‘opponents’ were various positions often called ‘Arianism’ and ‘Semi-Arianism’. These are imprecise labels and generally falling out of use among historians of this period.

I believe in one God, the Father almighty,

There is not too much controversial about the initial lines, the recognition that there is a single God is the defining element of Christian monotheism, and the epithet ‘Father’ is expected. Likewise ‘almighty’, or ‘omnipotent’ relates to his overall sovereignty. Uncontroversial.

maker of heaven and earth, of all things visible and invisible.

Again, not super controversial. It does exclude some gnostic doctrines, but I don’t think that is the primary aim here.

And in one Lord Jesus Christ,

The repetition of ‘one’ is part of the patterning of the Creed to assert that the Three are One.

the Only Begotten Son of God,

Now we are getting to some polemical texts. This line draws from John 1:18, which uses the word monogenes to refer to the Son as unique or one-of-a-kind. But it can also be translates ‘only-begotten’; the 4th century debates revolved a great deal about what that meant, and the pro-Nicene parties eventually came to take it to mean ‘the only one who is Begotten of the Father’.

begotten from the Father before all ages.

‘begotten of the Father’ here it refers to the causal origin of the Son from the Father. The Cappadocian Fathers were particularly careful to argue that the relationship of Begetting/Birth/Generation was stripped of its material concepts. ‘before all ages’ functions to mean something like, ‘before the beginning of temporality itself.’ It excludes the causation of the Son from temporal respects.

Both of these factors are anti-heresy. They oppose positions that said either (a) that the Son was not ‘of the Father’ in a causal sense or a ‘being’ sense (typical of late Anomoian or Heteroousian theology), and/or (b) that the Son’s coming-into-being took place either (i) in time, or (ii) prior to the beginning of time but still in-a-way-temporally after the Father’s existence.

God from God, Light from Light, true God from true God,

While for most English speakers, ‘God’ just means (even if one doesn’t believe in his existence), a singular all-powerful being radically distinct from creation, the Greek term θεός (theos) didn’t necessarily bear that sense. So that some heterodox groups in the 4th century happily called the Son ‘god’, but ‘not God like the Father is God’. This phrasing here is designed to exclude those positions, not only ‘God from God’, but ‘true God from true God’. Secondly, they emphasise that because the Son is ‘of the Father’ he is just as much God as the Father is. ‘Light from Light’ partially refers to the standard use of light as an analogy for this – light caused by light is still the same light.

begotten, not made, consubstantial with the Father; through him all things were made.

The important contrast ‘begotten, not made’, plugs again into those 4th cent. controversies. For Arians positions ‘begotten’ when referring to the Son actually means ‘made’ – the Son was created by the Father, ‘but not like the other creatures’. This line deliberately excludes understanding the Son as a created entity. This is complemented by ‘consubstantial’, a technical term (often ‘of one being’) indicating that the Son has one and the same ontological ‘essence’ as the Father does.

The last phrase here echoes John 1:4 and refers to the Son’s mediatorial role in creation.

For us men and for our salvation

He came down from heaven,

and by the Holy Spirit was incarnate of the Virgin Mary,

and became man.

This moves the creed from the theology-proper of the Son, to what the Fathers called ‘the economy’ – God’s acts towards humanity and in history, primarily in Jesus and towards salvation. This lines are not super-controversial. Though the understanding of salvation among the pro-Nicenes and Arians was quite different.

‘Became man’ is important, in that the pro-Nicene understanding was clearly of a fully-human, fully-divine Christ, who always was God, then became both God and Human, and later that humanity in him was deified. It is not, however, concerned with monophysitism, or the theotokos debate, which are 5th century concerns that are anachronistic to imply in the Creed’s historical context.

And was crucified for use under Pontius Pilate,

and suffered and was buried,

and rose again on the third day according to the Scripture

and ascended to heaven, and sits on the right hand of the Father,

and will come again with glory to judge the living and the dead,

of whose kingdom there will be no end.

The most significant phrase to comment on here is the last, ‘of whose kingdom there will be no end.’ This ‘rider’ was added to exclude the theology of Marcellus of Ancyra, who understood 1 Corinthians 15 to teach that Jesus would hand the kingdom to the Father and cease to be king. This, coupled with other things in Marcellus’ theology, led to his condemnation, and this part of the creed explicitly excludes Marcellan theology.

I believe in the Holy Spirit, the Lord, the giver of life, who proceeds from the Father [and the Son,] who with the Father and the Son is adored and glorified, who has spoken through the prophets.

The final phrases deal with the third member of the Trinity, the Spirit, and explicitly title him ‘Lord’, which is indicating of his status as God. In the later parts of the 4th century debates there arose groups who accepted the Son’s divinity, but not the Spirit’s. They are sometimes called ‘pneumatomachoi’ (Spirit-fighters) or ‘Macedonians’ (after a leader, Makedonius; not after the place). Anyway, this label is designed to exclude their view.

Just as the relation of the Son to the Father was generally termed ‘Generation/Begetting’, the Spirit’s was called ‘Procession’. The addition of ‘and the Son’, the filioque, only occurred in the West, and reflects Latin and (R) Catholic theology. It is not accepted in the East (see E. Siecienski The Filioque: History of a Doctrinal Controversy for a full run down on it).

The ‘with the Father and the Son is adored and glorified’ continues to exclude Spirit-fighters’ views. It reflects the pro-Nicene view that the Spirit is equal in dignity, worth, and so honour, glory, and worship.

and in one, holy, Catholic, and Apostolic church. We confess one baptism for the remission of sins We look forward to the resurrection of the dead and the life of the world to come.

Not too much for me to add about the final phrases. ‘one baptism’ at this point in history excludes the Donatists, a movement primarily active in North Africa, who were known for rigorism, and felt that unless you had a ‘pure’ line of ministers who had never buckled under the pressure of persecution, then your sacraments weren’t valid. Hence > rebaptism.

I think that’s enough for now. So, yes, many phrases are anti-heterodox, because that was the purpose of the creed, and almost all those relate to 4th century theological controversies.

Further reading:

The text I used for the creed is a slightly edited version of JND Kelly’s in Early Christian Creeds. I’m happy to talk about the underlying Greek (or Latin) if you wish.

The single most defining book on 4th century controversies is RPC Hanson, Search for the Christian Doctrine of God. It’s a tome of massive length and not for the fainthearted.

The two best books on the emergence of Nicene orthodoxy in the 4th century are K. Anatolios, Retrieving Nicaea and L. Ayres Nicaea and its Legacy. Not light reads either, but certainly more accessibly than Hanson.

Edit: changed Jn 1:14 to 18 because I misremembered.

Are you talking about the Nicene Creed alone or the other ceremonial words surrounding it as well in certain ceremonies?