PLD: Save Fight or Flight and Circle of Scorn for the adds. Anything not already dead dies in 1-2 hits.
WAR: Overpower + Bloodbath.
Both Tanks: STR Accessories make all Alex maps utterly trivial.
BLM: Well, AoE.
SMN: Titan Tank Cyclops; deal with adds.
SCH: Let Eos do the healing. If all else fails, Eos will happily tank for you.
MNK, DRG, BRD, NIN: Their AOEs are sufficient.

General Tips
1. Stay close to the boss unless you're dodging AoE so you won't have to watch for Eye of the Beholder.
2. Try not to let both sets of adds out at once. Take them one at a time.
3. Bring an X-Potion. It can save you.