Bring out your Strider and finish him off with a Water Jet. Round 2, I swapped in Toothy.

I had Leatherhide runt out first and had him Trumpet Strike then smash repeatedly until Heliosus was about 1 hit away from going into his egg. Turn 4:

I am not expert on pet battles so there may be something out there way better, but for the amateur battler like myself, I found this combination of pets and strat to work absolutely great and I hope that it helps someone else out. Turn