From Stratics :

Leveling a crystal to stage 11 and 12

For stage 11 and 12 crystals there are the following changes:

1. You can only level a crystal to stage 11 and 12 on Anakim, Lilith or Dungeon Bosses.(Antharas, Baium, etc.)

2. An entire party can level up crystals to stage 11 or 12 at the same time. You do not need to drain or do anything else. You only have to make sure that you only have one crystal in your inventory (level 10 or 11) and that someone in your party gets last hit. So you can level up to 9 crystals each time you kill one of these bosses.

3. You cannot fail at levelling a crystal to stage 11 or 12 as long as your party got last hit on the boss. Note: Reflect Damage can get last hit.

Lilith seems the easiest to kill.
I'll find some info on Lilith and see what it takes to bring her down.