Fira/etc. aren't behind a lock, as far as I know. You just need to keep gaining sphere levels until you make your way over to the spells... you DO understand how to use the Sphere Grid, don't you? If you got this far without figuring that out, I'm impressed.

That said, you don't NEED those spells. Have an Aeon take the Mana Beam for you (have it use defend or whatever it is called) and use Wakka and Rikku to kill the Negator (Have rikku use electro or lightning marbles - you should have plenty if you were stealing on the Thunder Plains)