Sleep Sprout is in constant Auto Regen status. There is a high chance of an ambush to start the battle against Sleep Sprout, and it will begin with Goodnight inflicting magic-based damage and Sleep (by 99 turns), Poison, Berserk, Power Break and Armor Break. Goodnight will also be used as a counter to all physical attacks.
Being rooted to the ground, Sleep Sprouts have zero Evasion. Sleep Sprout's attacks will consist of the third-level elemental spells, along with Flare and Ultima. It has no elemental affiliation and is weak against Fire spells.
It drops weapon with status strikes and armor with status proofs, the Sleep versions of these abilities being fixed. Its equipment drops provide a 6% critical hit chance bonus instead of the usual 3% (this is relevant to weapons and armors, but only to attacks that deal physical damage).
For all except Ultima, using Reflect is a handy defense. As Sleep Sprout has less than 99,999 HP, a strong party member can kill it in one hit, making killing it the fastest way to farm Dark Matter from.
The best option is using the Celestial Weapons at full power (if available) for defeating him.