Floor 10: Iris
Floor 16: Devilkin x3
Floor 22: EX Harariel
On each of these floors, you need to break the parts completely on the enemies mentioned before killing them in order to get this trophy. Part health is shown when you perform attacks (often launcher and pursuit attacks) that also display a double-digit yellow HP sign. If you're over a certain damage threshold from your level, this might actually be hard to do. However, there are two options available to you:
1) I've read that you can use Galdo or Tiara's curing (Cure-All) spells to break the parts of enemies. I can't test the validity of this, but there is a better solution.
2) In the Evil Goddess route, you'll obtain a new character who has a special ability (Snipe) that targets just the parts. Two to three hits from this ability will break all parts on the target (any additional hits will damage the enemy, so you'll know when they're broken then).
For the Devilkin, you only have to break the parts off of one before killing it, rather than all three.