In the West we see the Persian empire as terrible people who tried to claim Greece. I learned later in life that they granted freedoms to most of its citizens and tested them with respect. My question is what is the truth and what is the bias of the Persian empire taught

Both views of the Persian Empire, specifically the Achaemenid Persian Empire, that you're describing are relatively extreme. It is absolutely true that the legacy of the Persians in the West has traditionally been as a barely-fended off evil Empire who would have prevented Literally Everything Good About Western Civilization. But there has also been a counterreaction to that, appearing both in general culture and in scholarship, that instead portrays the Achaemenids and their Empire as a precursor to the modern tolerant state; multicultural, religious agnostic, protective of individual freedoms, and safe/developed to live in, basically the Best Ancient State Ever.

Persia as Evil Empire

The first, more traditional attitude has a lot of baggage attached to it.

The fact is that this view of the evil Persian Empire only somewhat relates to the Greeks' own perspective. Herodotus is, considering his cultural identity and the fact that he was writing after the war had been won and changed everything about Greece forever, relatively even handed regarding the Persians when he discusses them. He's as eager to talk about Greek faults as he is to talk about Persian virtues, on the whole. It's still a biased, incomplete picture he paints of Xerxes, the Achaemenids, and their Empire, but that's not particularly surprising. We also have to reckon with the fact that most of mainland Greece, and the Greek islands of the Aegean sea, submitted to Xerxes willingly or were occupied with relatively little fuss. The fact that the Thebans, and the Boeotian League they headed, had sided with the Persians resulted in Athens basically annexing the entire region as retribution, and even after they had re-established themselves as a power in Greece people never stopped reminding the Thebans about siding with the Persians. The perspective of heroic victory against a barbaric invader is shouted all the louder because so many Greek states avoided or gave up this fight. Necessary evil or not, most Greeks did not consider this a fight for survival of their culture, or for their survival. The Spartans and Athenians had specific reasons for being Persian targets, the Athenians for helping the Ionian Revolt, and both of them for having killed Persian ambassadors.

We should also point out that by the 4th century the Greeks had formed a working relationship with the Persian Empire, both Athens and Sparta being willing and able to court the Persians for gold, fleets, and political support.

Persia as a great, evil, antagonist other has a lot to do with more modern reinterpretations of Greek and Roman attitudes. By the Victorian Era the study of the classical world in Western Europe had developed an idea of Hellenism, that is to say core principles of liberty, individual achievement, equitable government, and cultural/artistic/technological development. They saw this as having originated in Classical Greece, and as oppositional to what they termed despotic, oriental, inefficient Empires such as the Persians, or the successor states to Alexander such as the Seleucid Empire or the Ptolemaic Kingdom. In this idea of history, the notions of Hellenism were also taken up by Rome, who then unfortunately slid into superstitious despotism, who then passed on the seeds of Hellenism to western European cultures who then, in the Renaissance, emerged as beautiful liberated, advanced, free butterflies.

From the mention of 'oriental' above you will also perhaps guess this had something to do with the 19th-20th century Empires' views on race, empire, and cultural supremacy. They had formulated an idea of an 'oriental' character, characterised by superstition, lack of political will, lack of free will, submissiveness, and sensuousness. More than one academic and thinker postulated that this was what 'oriental' peoples had always been like, including the subjects of Empires like the Achaemenid Persians. The Persians were thus not simply an ancient people, opponents of the Greeks for a time, they were the precursors of peoples and states that the Western Empires had conquered or fought with. These Empires saw themselves, the British especially, as the direct heirs to the legacy of the Greek and Roman Empires. They also used racial ideas to justify the idea that these peoples should be governed. They supported this notion with the idea that all of these big, seemingly powerful eastern Empires had been ruled by despotic tyrants who treated their subjects as their slaves, and whose subject had no will or desire to overthrow their cruel masters. Battles like Marathon, Thermopylae, and Plataea stop being victories against a foreign aggressor, complete with cultural posturing by the Greeks, they become symbols of superior western attitudes and fighting prowess and nobility against faceless, savage, barely equipped masses of easterners led as slaves by tyrants.

Persia as Modern Multicultural State

At the time that it was founded, the Achaemenid state was the largest single state to have ever existed on the Earth, to our knowledge. It dwarfed its most powerful predecessor, the Neo-Assyrian Empire, and included most of western Eurasia's most urbanised populations. The Assyrians had to figure out a number of systems to govern their Empire, and they had already been the largest state in the Near East before starting their massive expansions in the 9th, 8th, and 7th centuries BC. The heirs of Cyrus inherited an enormous Empire practically overnight, and whilst they were happy to reuse existing systems they would improvise whatever could succeed at keeping their possessions pacified and prosperous.

So yes, we can talk about the Achaemenids having a multicultural state, by default. They conquered so many smaller kingdoms and states it was impossible for it not to be. But this was not a brotherhood of man willingly brought together, these were states brought into Persian rulership by conquest or by the futility of resisting it. The Persians had garrisons in most important cities of the Empire, and these troops were billeted at the locals' expense, oftentimes in the households of the very same locals. There were revolts against Achaemenid rule, mostly early in the Empire's lifetime, but beyond a certain point the Empire's military supremacy was almost completely uncontested. It is noteworthy that during Alexander the Great's campaigns, the only revolts against the Empire were those states who accepted Alexander's rule without a fight, and the seizure of the throne by the King's advisor Bessos, which only happened after a series of devastating losses and after the Achaemenid loyalists were reduced to Bactria, Sogdiana, and nearby territories. Not a single other bordering power attempted to invade the Achaemenids during this time either.

As for granting freedoms and treating them with respect, the Empire was so vast and complicated to manage that, with the material and social technologies of the time, the only way to realistically rule something of that size was to leave people alone in most respects of life. The Assyrians did exactly the same, on a smaller scale, and most large Empires through Eurasia's history have had to do some similar kind of decentralisation just to keep it together. It is true that the Achaemenids had no interest in controlling religious practices, or enforcing cultural norms, but they also had no interest in enforcing 'national' laws either because the concept simply didn't exist for large Empires at that point, and had no means of doing so. The Empire's authority and sovereignity was so concentrated in the figure of the King that the only 'national' law was whatever the King decreed, and the satraps who governed his provinces were appointees of the king, not titled nobility. The local Achaemenid administration would oversee local justice, and of course the real local governing was being done by governors and satraps rather than the King directly, but again these were responding to the practical requirements of governing such huge territories.

And as I said before, if the Achaemenids believed that cruel or severe behaviour was necessary, they were absolutely willing to commit to it. Executions, population deportations, conquest of foreign lands, sacking cities, destroying temples. It is never 'nice' to be in an Empire's direct path. Quotes about elephants and beds spring to mind.

The Achaemenids were sophisticated, flexible, and were willing to bend to other cultures in order to keep things running smoothly. But talking about them as a tolerant multicultural state in such glowing terms is trying to bend too far the other way. As with a number of dubious historical interpretations, the counterreactions in their eagerness are often themselves hyperbolic or hagiographical. The association of powerful, 'real' Empire with the Greco-Roman tradition, and the Achaemenids as a charicatured other, has also encouraged people to see the Persians as an opposition to what they see as a western style Empire. They also see traits embodied in the Achaemenids, like a nonchalance about personal behaviour, personal religious beliefs, and the free mixing of utterly different peoples on an equal basis. These traits appear more positively to them, and more similar to a modern multicultural state, than the qualities the Romans and Greeks perceived as best about themselves, or the western Empires perceived as best about themselves either. The Achaemenids don't resemble their historical charicature, but it's entirely possible to reject that without making them into saints taken from us before their time. That just leads to a different charicature that's more positive but no less wrong.

The Achaemenid monarchs were people, complex and intelligent and ambitious, and their Empire was a human creation, sprawling, diverse, founded on conquest and a belief that some amount of human suffering was necessary to keep stability and peace. I think that does justice to them.