The Split Personality achievement is an endurance test. The main mob alternates between two names -- Avatar of Ladrys, Avatar of Sholoth. I off-tanked this mob at the beginning of the mission until I counted 20 changes between the two names which took 16 minutes. Your target doesn't change, just the name of the NPC and the color of its robe. You could also do the off-tanking near the end of the mission instead, if you want. Put damage mercs on hold, and put cleric merc on efficient or on hold to save mana.
This achievement is awarded when you open the chest at the end of the mission.