Beat a Boss with no Damage Taken
There is a broken sigil called [Glazed Aegis], which can be collected in the middle part of the game. It provides a barrier after an use of healing bell.
The barrier can block ALL damage from one hit, and it lasts FOREVER if you don’t get hit (it will disappear if you remove the sigil).
If you are hit when you have a barrier, you can still achieve No Damage Taken. And you can create the barrier many times during the battle according to the amount of your magic points.
That means you can easily get the achievement from any boss after you get the sigil.
However, I recommend to try every boss without this sigil, because it may just ruin your game experience.