The most easy method of obtaining a first limit break is by fighting in the forests outside Junon or inside Mythril Cave with that particular character equipped with the Choco/Mog materia. Get into a battle with 4/5 enemies and use that character to cast Choco/Mog for an instant kill to all (Choco/Mog is basically enough to kill off all enemies at once, being able to do 500-800 damage in my case including the fat Chocobo attack and only consumes 14MP) enemies. Repeat process on all characters i.e. focus limits on one characater at a time.

To get the second limit go to Mideel and fight the monsters there. They deal a considerate amount of damage to fill up your limit gauge. If you think you are a hell of a tanker, the Sunken Gelnika is preferable as the monsters there deal an insane amount of damage. For a normal monster.