Let's start with the obvious: Achieving the Grand Master rank, whether it's the comparatively simple GM rank in the original TGM or the world-class GM rank in TGM 3.
One player achieved GM rank in The Absolute PLUS on an emulator, but a few technical screwups altered the RNG seed of his replay, screwing it up. Fortunately, he and the TGM community were able to fix his replay, allowing him to upload it on YouTube.
KevinDDR, a western TGM 3 Player, being the FIRST Western player to become Classic GM! Watch here!
In TAP, getting the RE (Recovery) medal, which requires first having 150 blocks in the playfieldnote the playfield is 10 cells wide and 20 cells tall, for a total of 200 cells. In other words, 75% of the playfield must be stuffed with blocks. and then dropping back down to 75 blocks.
Also in TAP, completing Doubles mode. Due to the game forcing 20G on the first player to reach level 300 in a mode where the playfield is extra wide, playing Doubles requires both players to work together with a strong sense of cooperation.