I've found the easiest way to unlock this prior to the endgame grind is through an Aeon's overdrive ability. Aeon's damage is based on Yuna's magic and strength stats, so be sure to keep her active in your party throughout the game to level her up. They will hit 99,999 damage with an overdrive long before your regular characters do.
In order to unlock the break damage limit on the aeons and do 99,999 damage, you need to power up a certain character's ultimate weapon for the first time. For the achievement, only 1 hit of 1 aeon's overdrive would need to do the 99,999 damage, so not all of these are needed.
Valefor - Yuna's Nirvana needs to be powered up with the Moon Crest
Ifrit - Wakka's World Champion with the Mercury Crest
Ixion - Kimahri's Spirit Lance with Jupiter Crest
Shiva - Lulu's Onion Knight with Mars Crest
Bahamut, Anima, & Magus Sisters start with the break damage ability.
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