Note: Some of the enemies (for example, the Ronsos) can only be fought once, so be sure and get them when they come. Also, some other places become unavailable after passing through them (i.e., Home), or lose their enemies (i.e., Luca). So please be careful about those. Also, some monsters (such as the Great Malboro) can be found in more than one area. For best results, I would say use the Calm Lands Training Area.
Kilika
Ragora
Seed Cannon
Mi'ihen
Bomb
Self-Destruct
Dual Horn
Fire Breath
Djose
Basilisk
Stone Breath
Macalania
Chimera
Aqua Breath
Sanubia
Sandragora
Seed Cannon
Home
Bomb
Self-Destruct
Dual Horn
Fire Breath
Chimera
Aqua Breath
Airship
Dual Horn
Fire Breath
Bomb
Self-Destruct
Bevelle
YKT-63
Thrust Kick
Calm Lands
Chimera Brain
Aqua Breath
Malboro
Bad Breath
Anacondaur
Stone Breath
Cavern of the Stolen Fayth
Ghost
Doom
Valaha
Fire Breath
Mount Gagazet
Grat
Seed Cannon
Yenke Ronso
Fire Breath, Stone Breath, Aqua Breath, White Wind
Biran Ronso
Self-Destruct, Thrust Kick, Doom, Mighty Guard
Dark Flan
White Wind
Grendel
Fire Breath
Grenade
Self-Destruct
Behemoth
Mighty Guard
Zanarkand Ruins
Dark Flan
White Wind
Grendel
Fire Breath
Behemoth
Mighty Guard
YKT-11
Thrust Kick
Sin
Great Malboro
Bad Breath
Behemoth King
Mighty Guard
Wraith
Doom
Omega Ruins
Omega Weapon
Nova
Puroboros
Self-Destruct
Spirit
White Wind