From what I gather, Moogle Mastery works on an experience points-style system where each tracked stat contributes points towards leveling up. However, regardless of how much "experience" you have, you need to fulfill certain prerequisites to raise your maximum level (think "limit break"). The below lists are these "limit breaks".
Any additions and corrections are greatly appreciated.
Sheol A
Kill 1600-2200 Nostos monsters
Kill ? total NMs
Open a combined ? boxes
Open ? Chests
Open 16 Coffers
Open 16 Aurum Strongboxes
Kill all NMs 6 times
Sheol B
Kill 1600-2200 Nostos monsters
Kill ? NMs
Open a combined ? boxes
Open ? Chests
Open 16 Coffers
Open 16 Aurum Strongboxes
3 NMs with 3 kills
6 NMs with 3 kills
9 NMs with 3 kills
12 NMs with 3 kills
15 NMs with 3 kills
18 NMs with 3 kills
21 NMs with 3 kills
24 NMs with 3 kills
Sheol C
Kill 1600-2200 Nostos monsters
Kill ? NMs
Open a combined ? boxes
Open ? Chests
Open 16 Coffers
Open 16 Aurum Strongboxes
9 Asena kills
9 Bygul kills
9 Chaos Steward kills
9 Dabbat al-Ard kills
9 Kurmajara kills
9 Lotanu kills
9 Wayra Tata kills