Unlike every other character, Cait Sith only has two limit breaks, and no limit manual to teach his final limit break. You don't even need to use his limits - getting 40 kills will teach Slots and unlock the achievement, and you can do this immediately after recruiting him. The fastest way to get this is to have an Enemy Skill materia with Matra Magic, an 8 MP multi-target non-elemental spell.ENEMY SKILL AND MATRA MAGIC LOCATION
Playing normally, I put Cait Sith in my party as soon as I recruited him and got the 40 kills by the time I reached Rocket Town. Alternately, my preferred limit level spot is the forest just east of Junon, which consistently has 3-5 enemies that can be burned down with Matra Magic. If you need to rest, Fort Condor has a free inn.