For the ice cave boss, I used the capital's thunder and wind runes, the snow village's fire rune, and equipped the magic staves to give access to healing/dark/earth buffs. Weapon I think I'd looted from the cave, but I tend to prefer the red rods for their 10TP/hit and multi-hit boosts. A scythe might also work with their damage boosts, but you're rushing damage much harder due to their 3TP/hit recovery.
Buff up and fire off your instants, thunder attacks will do by far the most damage to it and don't be afraid to just attack to store TP.
As for speed, the 33TP skill makes you act 1st regardless of speed I believe, the one that adds 4 hits to your basic attack.