BASICS OF LIMIT BREAKS*** Spoiler - click to reveal ***With the exception of the final, each level of limit breaks are unlocked in two ways. To unlock the second limit break, keep using the first one. To unlock the next level, get killing blows on enemies. Killing blows are cumulative over a save file and DO count before you reach the level.
Using the in-game cheats is allowed, so you can turn on Battle Assist to speed up using the limits. A good place to farm kills early is the forest east of Junon, as you can reliably get 3-5 enemies that can be taken out with Matra Magic or a basic magic with All materia. Late in the game, the forest at Mideel has 3-4 that can be taken out with heavy-hitting Enemy Skills and also doubles as a decent AP farm. The exact numbers needed are below.
1-2: Clear Tranquil - Use Greased Lightning 8 times
2-1: Landscaper - Get 64 kills.
2-2: Bloodfest - Use Landscaper 7 times.
3-1: Gauntlet - Get 128 kills.
3-2: Doom of the Living - Use Gauntlet 6 times.
All Creation is obtained by completing the Pagoda sidequest. This is also done as the sidequest to get the Leviathan materia, which is a separate achievement.