WARNING: Spoilers for Final Fantasies 7, 8, 9 and X ahead
Random encounters:
3) Varuna (Final Fantasy X) - I don't really know why. He's just fun to fight.
2) T-Rexaur (Final Fantasy VIII) - A super powerful monster who can be weakened with strategy, rather than just requiring super defence. My type of customer.
1) Great Malboro (Final Fantasy X) - A battle where power means almost nothing and strategy is everything. What more could I ask for?
Storyline bosses:
3) Seymour Omnis (Final Fantasy X) - The mortiphasms are really fun to play with, although the battle could've been pulled off better. Try beating him without ever attacking him, by using Reflect and playing with the mortiphasms. It can be done.
2) Yunalesca (Final Fantasy X) - Another one where strategy far prevails over brute power.
1) Bizzaro Sephiroth (Final Fantasy VII) - The switching parties, multiple targets with different functionalities and needing to figure out exactly how to deal with them. A great battle.
Optional bosses:
3) Hades (Final Fantasy IX) - I consider this guy to be the real "ultimate" boss of FF9, as Ozma is purely a matter of luck. A good fight, which can still be set in stone with good strategy.
2) Omega Weapon (Final Fantasy VIII) - No invincibility, no The End... try beating him this way. Another fun and strategy-filled battle.
1) Dark Bahamut (Final Fantasy X) - Occasional counterattacks rather than abusing them, decent attacks rather than insane ones that require either hundreds of turns to prepare or lots of luck to survive, and a decent but not overkill amount of HP. This is not only my favourite optional boss, but my favourite enemy full stop from any Final Fantasy I've played so far (which are 6 to X-2).
Finally, for No Sphere Grid + No Summon + No Doom Optional Bosses on Final Fantasy X:
3) Catastrophe - Requires a good amount of switching and thinking to work out and near the start, but only gets 3rd as towards the end it just gets extremely tedious.
2) Jumbo Flan - Even more strategic, and actually requires on-the-spot strategy all the way through unlike Catastrophe who's just a matter of getting the setup right.
1) Omega Weapon (PAL/Int) - You say he's pathetic? Try fighting him this way. He's not unreasonable (you need a little bit of luck but if done right you can usually win) or overly long (the battle lasts 15 to 25 minutes), but still requires a good amount of planned and on-the-spot strategy, effective character switching (including use of placeholder characters) and planning ahead. Probably my favourite battle so far in this challenge.