Fast materia level-ups
Go to the Northern cave and look for mole-like creatures with a star above their heads, holding a knife and a lantern. Steal an elixir from them and run away, then look for these small creatures in a floating pot. They will say "Gimme' an elixer". Give them one, then kill it. Each one killed will give you 1,000 AP. You cannot kill them unless you give them an elixer.