This is a common enough grouping of titles to appear on, say, Wikiquote, but the oldest academic source I can seem to find on it dates from 1772—it’s also in German, which I only know enough of to discern that the same titles are present.
Which ancient author was purported to have attributed all these grandiose titles to everyone’s favourite Late Antique steppe conqueror? Furthermore, what’s with the claims to rule the Danes and Medes, with whom the Huns barely interacted with in reality, if at all, not to mention the whole “descended from Nimrod” business?
EDIT: It’s been pointed out to me that the German source reads “Dacians” for “Danes”, which makes a lick more sense.
UPDATE
I've done a bit more digging around, and the Reverend William Herbert attributes this titling of Attila to a certain "Nicolas Olaus" and explicates that the presence of "Nimrod", "Engaddi", "Medes" and "Danes" were all intended to reference apocalyptic imagery from the Bible, with the Danes and/or Dacians standing in for the lost tribe of Danites (p.21-23).
Although Herbert calls Nicolas Olaus a "13th-century writer", he, Nicolaus Olahus, was in fact a 16th-century priest and politician whose work being quoted is almost certainly Hungaria et Attila - I can't find an online translation, but it is described as being pretty much explicitly written with nationalistic and religious fervour, hence the exaggeration of Attila into an apocalyptic figure.
The oldest Latin original for these titles I could find was this, in which "Dacorum" (Dacians) and "Danorum" (Danes) both appear [EDIT: This 1580 book by a certain Franciscus de Rosieres about the history of Lotharingia seems to have the titles in full.]
With regards to the title "Scourge of God", that appears to date only as early as the Golden Legend's chapter on St. Germanus—that said, Jordanes, a near-contemporary, does call him “The Scourge of All Lands”, so it’s not that far off.
So, is there much reason to believe there was much in the way of these titles prior to Nicolaus' Hungaria et Attila?
Pretty close and sometimes exactly the same description is found about Atilla in the Hungarian chronicles (For example in "Kálti Márk: Képes krónika" / Cronica pictum from the XIVth century). Many of these work from earlier sources and there are earlier chronicles with this title.
So weird no one talks about them here in this topic, because they clearly have this information in it.