VERY IMPORTANT! PLEASE READ:This is not a guide, but an important note to anybody trying for this achievementOn both the achievements app and the milestones page of Battletoads arcade, you will see this achievement and it should have a percentage (%) under it. Everytime you complete a playthrough with a different character, the percentage should go up 33% or 34% in this order:
0% (no playthroughs completed yet), 33% (1st), 66% (2nd), 100% (3rd and final)
^common sense^
However, many of us have completed the game multiple times but our % are stuck behind.
For example, I completed the game 3 times with all three toads but the percentage says 33% (only one playthrough completed), on both the milestones page and the achievements app.
Proposed SolutionWhenever you've completed a single playthrough, hold

to load up the pause menu, and select Load>New Game, and start your new playthrough on a fresh save file. I can confirm this worked for me. Should work the same for you!