~Complete the Sphere Grids for all main characters~

This trophy is the most time-consuming trophy in the game. It requires you to fill up every single node on the Sphere Grid with a stat enhancement and then have all of the characters activate every single node on the Sphere Grid. This will require unlocking all Sphere Locks and grinding stat spheres from the Monster Arena to fill in the Sphere Grid. This trophy can be made slightly easier by choosing the Expert Grid over the Standard Grid, as the Expert Grid has fewer nodes to fill up.

The main problem with this trophy is getting everyone Sphere Levels so they can move around the Grid. There's a method to quickly gain Sphere Levels involving the Monster Arena. First you should unlock and fight One-Eye at the Monster Arena until he drops a character's weapon with the Triple AP ability and one to two empty slots. He's unlocked by capturing at least one of four different types of Floating Eye enemy types. With that in place, customize the weapon with the Overdrive -> AP ability and the Triple Overdrive ability. With the weapon equipped, put your character on Stoic Overdrive Mode.

Now in the Monster Arena fight a Don Tonberry. When the Tonberry is far away he'll counter every attack with his Grudge that does 100 damage for every kill that character's made; this can stack all the way up to 99999 damage. If a character gets hit for maximum damage they'll earn a boatload of AP and earn immense Sphere Levels at the end of the battle, especially when hit multiple times. You should note that once the Tonberry gets 4 turns he'll be too close to counter-attack with Grudge; from here you can finish him off or run away and still get your AP.

To optimize this process your party should be equipped with armor that has Auto-Phoenix and Auto-Haste. This allows your party to automatically revive the character who dies and they can get multiple turns in before the Tonberry gets too close.

If your character isn't getting hit that much by Grudge, you can farm kills with them at the Monster Arena by using a controller with auto-fire or by simply going to low level areas and earning them kills. If that's too boring for you, you can keep that character's weapon equipped then go to Omega Ruins and grind kills there. Just be sure they get at least one turn or they'll get no AP.

One final note is when you think you're nearing the end of a character's grid, select a Master Sphere and use it to scan for any possible missed nodes. You can use it to activate a node from anywhere on the Grid, but they're rare so try to conserve them and keep them to check for any missed nodes.