Earthgift Shrine is actually an optional dungeon, as are Hellfire Chasm, Lifespring Grotto and Whisperwind cove.

These are all bosses form FF III, and you only will need to beat one of them. To fight the others you have to go through the dungeon again a total of four times. If I recall correctly, Echidna uses lots of instant death attacks, 2 Headed Dragon and Cerberus hit with physical attacks, and Armiham I don't really remember but I did beat him last. Go with whichever one you find easiest to handle.

Black mages/wizards should only use Temper and Haste on your main attackers, Temper can be cast multiple times and the effects stack. White mages/wizards should be healing your attackers (don't want to lose all those tempers), throw around protects when they can. red mages/wizards can do either task, use as needed. A ninja can also use temper to help if you have one. Everyone else should attack.

Also for the future, the bosses in Lifespring Grotto are the FF V bosses, and the two on the final floor are Shinryu and Omega, and they are harder than the bosses in Whisperwind Cove.