This was the first big stumbling block for me too. After getting demolished a few times using my preferred tank/heal type pets, I went out and leveled up a Darkmoon Zeppelin for the bear, and a Phoenix Hatchling for the Mechapeep. I suspect that almost any elemental would have made the Mechapeep very easy.
If you don't want to level an elemental, I'd suggest something with an evasion-type ability (lift-off, burrow, soul ward, there are many possibilities out there). The Mechapeep telegraphs his biggest move--I think it's called Windup--so you can get out of the way. You will probably appreciate having this for Courageous Yon in Kun-Lai Summit as well.



