messed around with crab battles game in the arena.
Saucy traps are useless. It's much easier to just use rarity stones on your choice of crab. Evolving at higher levels will not net any gains, just evolve at level 30.
I found that skills only really matter when enemy has huge level advantage. The only 2 that are useful are Poison(significant damage amp), and Confusion(chance to not get attacked). Enemy usually will just try to use stupid skills, while you just use normal attacks with advantage if possible. Fire>Water>Earth>Fire.
Crabs seem to have preset stats, since you're mostly attacking, attack is the better stat to have, but choices are limited as crabs have specific elements:
Air: Just Doo'AHLAI, it has HP/Atk, and Confusion.
Earth: Just Jacko, HP/Acc, but it has Poison.
Water: Clawp, Even stats, and Poison.
Fire: No choices, only Slycer or Slasher, they are both Atk/Acc, and have no good skills.
Battles are pretty basic: Swap to appropriate element, basic attacks, potion if necessary, generally ignore status.