I've been trying to find a reference to the haste spell in Final Fantasy 13-2 but I can't find it anywhere. It doesn't seem to appear on any of the character spells for Synergist, does it appear on any of the monsters?
Haste, as it existed in Final Fantasy XIII, doesn't exist in Final Fantasy XIII-2. Instead, the Mog clock is the primary source of haste: if you get a "Great!" rating, you'll get a preemptive strike and start the battle with haste.
There's also a commando auto-ability for monsters, Haste Feeder, that casts Haste on the monster automatically.
A number of weapons and accessories that increase the ATB rate:
- Faerie's Bow, Rune Feather, Angel's Bow, Eurytos's Bow, and Indrajit for Serah
- Rune Tooth, Sargantanas, Nomad's Machete, Orochi, and Romulus & Remus for Noel
- Kaiser Knuckles line of accessories
The Hermes Sandals line of accessories also casts Haste when critical.