About the fights you cannot avoid.

Plant Spiders: Kill Zidane, Vivi and Steiner. Blank kill the Spiders and LvUp to 3 (BUT it means that Amarant will come at Lv3.) If you get 2 Spiders, kill them wuith everyone alive. No one will lvl up then.

Black Mage x2, Gizamaluke: Pain in the neck. Quina in the back row, with the Needle Fork of Zaghnol, and Add Status. Have him attack the Black Mages to TRY to Petrify them. Quina can't kill them in one shot so it's safe. After Quina caused 200+ damage to Black Mages and they are still alive, use a Potion on them. Revive dead members with Phoenix Down.

Black Mage x2, Burmecia: Same as above, but Vivi has Stop (Oak Staff from Chocograph "Small Beach" so it's easier.

Alexandria Soldiers and Black Mages, Cleyra: Same as above. Or dealdamage to the solders without killing them. When their HP is low enough they will flee.

Well, since I stopped here, that's all I can help you with. XD