DJMAX RESPECT V

This achievement is the hardest to pull off in the base game without any DLC. There are a total of 60 missions, and only 1 of those has an A.I opponent, which happens to be mission 54 "SSS" in the D-velopers category. This mission requires you to play 4 songs against the A.I and beat their total score of all songs combined by the end of the mission.

The 4 songs you need to play against the A.I are:
[4B Hard] A.I
[5B Hard] Brain Storm
[6B Maximum] My Alias
[8B Maximum] Chemical Slave

What makes this absurdly challenging is the final song of the mission, Chemical Slave. In order to beat the A.I on each song you need to get what I would estimate around an 97-98% average rate. So in order to beat the mission you'd need to be good enough to pretty much get an S rank on Chemical Slave's 8B MX chart, which is *very* difficult sitting at a difficulty of 14 stars, and is more difficult than any of the other 50 missions you'd need to unlock the BEAT MAESTRO achievement.
Here's a video of what this chart looks like:
Aside from being decent at 8B, there are strategies you can use to make this last song a bit easier. Since the score carries over between songs, you'd ideally want to put as much of a lead as possible between you and the A.I during the first 3 songs, aiming to Perfect Play them or get as close as you reasonably can to a 100% rate. Another thing to note is that unlike regular ranked matches, in this match against the A.I both of you are using Auto 5x Fever. While Fever does increase your combo, it also increases the score you get for every note hit a little bit, so ideally you'd want to keep the 5x fever for as long as possible during the first half of the song, even if you happen to miss a lot in the second half. Fortunately you can retry Chemical Slave without needing to redo the other 3 songs, so you can just use the mission itself rather than loading the song up in Freestyle if you need to practice.

Now, the reason why I had to clarify that this is the hardest base game achievement without owning any DLC is that with the Trilogy DLC pack comes an additional 12 missions. And mission 4, "Electronic License" also requires you to play against an A.I. The main difference with this mission is that there is only 3 songs, the hardest of which is Nevermind on 6B Normal, which is substantially easier than Chemical Slave. So if you aren't quite up to the level of S ranking 8B MX songs, buying the Trilogy DLC is a significantly easier option.

There are also other DLCs that have A.I., namely V Extension, Clazziquai, Black Square, Portable 3, V Extension 2 and V Extension 3 (with maybe more to come) however those are still relatively hard to clear, so Trilogy is the one to get if you're just concerned with getting all of the base game achievements.