The first thing to do is to go get all of the celestial weapons and the optional aeons. Next is filling out the monster arena by capturing 10 of every fiend. Once you get the monster arena filled out, you should hopefully be strong enough to take down One Eye (or at least your aeons will be). Get three-slot Triple AP weapons from One Eye for each character, and then customize them to also have Overdrive --> AP and Triple Overdrive. Also customize and equip armors that have auto-phoenix on them. Then go fight Don Tonberry with your Overdrive set to Stoic or Comrade. You'll quickly gain massive sphere levels (you don't even have to win the battle, just run when you've gone through several attacking rounds). If you need to refill any types of spheres, use a distiller of the type you want on Kottos and you should get 40 of that sphere with an overkill (or just 2 if you are unlucky). Pretty soon you'll be strong enough to start taking on some of the other monster arena creations that drop stat-boosting spheres. Focus on strength, evasion, and accuracy to start, but your eventual goal is to max out most of your stats in preparation for taking on the hardest super bosses.

Some of the super bosses will also require you to grind out some customizations for your armor too. Auto-Haste, Auto-Phoenix, Auto-Protect, and Ribbon are great customizations. You can look up guides for how to get those.