Solo Tifa vs Crimson Mare Mk. II (Hard Mode, No Hit*,

Dragon Claws - Attack +20, Attack +20, ATB Charge Rate Up, Weapon Ability ATB Recovery
Fury Ring
Cetran Bracer
Elemental-Lightning, Enemy Skill-ATB Boost, Strength Up-First Strike, Odin
Elemental-Fire, Swiftcast-Lightning, Magic Focus-Lightning, Time-Steadfast Block
*Technically, I got shot on the run up to the boss. I tried quite a few times but I actually took damage more often than not on the run up? A little annoying.
Again, for speedkill purposes, our goal is to get the Crimson Mare to as close to staggering as possible without staggering, and transitioning to phase 2 (or technically, phase 3, if you count the Mako gauntlets as phase 2).
You can instantly pressure the Crimson Mare if you Thundaga each gauntlet, usually.
Elemental Fire is for the bombs she lays down once both gauntlets are destroyed. It's easiest to just tank those the bombs and keep pressuring :P
I actually have faster runs but I got chipped on some of the gun attacks :(