How do the 9999 and 99999 limits work?

[Tavrobel]

Break HP Limit ability, armors only.

The ability is synthesized using Wings to Discovery, a drop from the Shinryu Monster Arena Original Creation, 1 for kill, 2 for Overkill. Alternatively, you also receive 30 from completing Remiem Temple Chocobo race under certain conditions (once only), and you can Bribe them from Marlboro 540k for 3-5, or Greater Marlboro 1.28 million for anywhere from 6-10, 8 being the average. I assume you're using NTSC, not PAL.

A 3Os version of this armor with BHPL is often dropped from the higher Original Creations, most namely of them, Nemesis, and Omega Weapon of the Omega Ruins. I've heard that it is possible to drop 4Os, but I have never actually seen it myself. Simply buy a Tetra Armor from Wantz in South Macalania, and make the armor yourself if you want all four slots for customization. They are fairly cheap.

To break Weapon Damage Limit, you need the Break Damage Limit, which is synthesized from 60 Dark Matter, a drop from all of the original Creations as a Rare drop, ranging from 12.5% to 25%.

All damage and HP for characters is capped at 99999.