Once you're in the game, make sure you're in the main menu with all of the songs. Then, go to your profile and select your Dancer Card. Now you just have to change the alias 20 times.
1.) Switch to a different alias after selecting "Alias" from the Dancer Card menu.
2.) This part is automatic. The game will automatically save it for you. However, upon doing this, it returns you to the main Dancer Card screen. This is probably the only thing interfering with your progress towards your achievement and adding any actual difficulty to it.
3.) Simply select "Alias" again and repeat. It actually couldn't get easier than that; For real.
You can do any Alias you want. It can even be "The New Dancer" and "Remember Me". "The New Dancer" sounds pretty cool and is likely a good description of you, and "Remember Me" sounds epic. Use a couple cool ones, switch it up or do whatever you want.
Note: Record scratch! Wait a minute. Did you think following this guide was making you vulnerable? Of course not. Actually, you can throw in a twist to it. One thing you should try is to end on "Remember Me" when unlocking the achievement. This would make for an epic ending on par with the song "Lacrimosa". Feel free to go for an epic ending. Do whatever you want. Feel free to get creative.