It might be worth mentioning that the
battle track DLC for DMC5 lists it as "Public Enemy (Dante battle theme 1)."
Then again as mentioned before you have titles like "Final Penetration," "Blue Orgasm," "I'm Coming!" and "Bloody Bladder" so the double entendre was probably intentional.
Regardless, I'm quite glad they finally released official English translations for the soundtracks even though I disagree with a small handful of said translations. I don't have too many complaints regarding the translations as far the DMC1 OST goes. I think it's a little odd that they went with "On My Father's Name" over "Swearing On My Father's Name," but I suppose it still means the same thing either way. Personally I would have gone with "Garden" over "Gardens" since I believe that the whole area in Mission 9 would just count as one large garden as opposed to multiple, plus that's what the Brady Games strategy guide listed it as.
The only two translations I really question though are the ones for 2.15 and 2.16.
Track 2.15, "魔界大神殿" plays in the chapel area where Mundus' physical form resides. I'm not really sure how they got "God of the Demon World" out of that unless they were just taking a lot of liberties with it.
A more accurate translation would be "Underworld's Great Temple." The
Devil May Cry Sound Box (back when it was still available on iTunes) listed it as "Hell's Great Temple" which would also be correct, but "Underworld" would be more internally consistent.
It's also weird how it's the only time in these new translations where they used "Demon World" instead of "Underworld." Also, while it's true that Mundus' exterior appearance is that of a godlike deity I don't believe he nor anyone else ever refers to him as being a god, they just use titles like "king," "emperor," "master," "prince of darkness," etc.
Track 2.16, "策略" actually can be translated as "tactics," but in context I think the translation used on the Sound Box, "A Scheme" is more appropriate.
For context, this played in the
cutscene where Mundus used Trish as leverage against Dante in order to ensure his victory. While "tactics" is still applicable to the scenario, I feel that "scheme" gets across the underhanded nature of the situation better as tactics lacks that same connotation.