Can be done on any difficulty.
The first boss fight which is song #4 or so makes you use your Chi (LB/LT ability that raises your multiplier) in order to defeat the boss. You must build up your Chi by hitting enemies correctly (and not getting hit since that takes away your Chi) and press LB/LT when your Chi is completely full.
In order to defeat the boss, you must hit him 5-6 times, and then finish the rest of the song. If you don't hit him enough by the time the song ends, you will lose. This achievement will unlock no matter how bad you do during this fight.