Araxia is backed up by Big Bones in this fight. While they both have 4,000HP, you can only attack Araxia.
I recommend that you be sure to buy all the stamps offered in "Grubbins on Ice". For this battle I think you should use a strong offense like Skeleton of the Wolf with your favorite attack costume. Next I recommend your healer be equipped with the Multi-Wing Bat stamp, as it will regen the whole party. It is imperative you use the Yeti costume, as it can shield the whole party from harm; Big Bones will eventually start attacking and the stamp will keep you alive. I equipped the Yeti with the strongest single attack poison I had.
* Attack costume - strongest attack stamp (Skeleton of the Wolf or such).
* Yeti costume - strongest poison stamp.
* Healer costume - Multi-Wing Bat stamp (full party regen).
With the above combo I attacked Araxia. After a few rounds of hitting him he will have candy fed to Big Bones, which will cause him to attack. You need to have the Yeti's shield up to avoid major damage. The damage increases every time Big Bones attacks, so you will be wiped out in a long battle no matter what.
Araxia will eventually adopt an airborne defensive posture. Skip your special moves, he won't take damage; but he will be knocked back! Three attacks will knock him back into the path of Big Bones incoming candy, disrupting the attack for that round.
Eventually when you get Araxia's HP down to 1, he will go into his airborne defensive posture again. From here, you must knock him into Big Bones to win the battle!
Congratulations, you have now beaten "Grubbins on Ice"!