Hydross: Keep it on hydross, pull it back a few seconds before a phase switch and send it back in after the tank has it while you help with adds.
Lurker: place your pet on stay on the main island in front of the small island where you'll be standing.
If you can hit it with Mend Pet, there is no reason why it should die.
Leotheras: Ok, now this is an annoying fight, you'll basically have to pull back your pet whenever the melee has to run.
And that's often, very often.
For the demons, I dont bother with sending my pet at them, they're a joke to kite and kill and my pet stays on Leo.
Karathress: nothing special here, just send it in on whatever you are killing, might need a few mend pets but I cant recall my pet dying here.
Morogrim: nothing special here either just fire and forget, though you might have to resummon your pet after you've been graved depending on where you tank him.
Vashj: Send it after whatever you're trying to kill. It'll probably require a bunch of healing but hopefully you'll have 2pc T5 by then to help you.
As for loot, Leo's trinket for 1 is something you'll want.
The chest from Hydross is also better, and you'll want either T5 legs or gloves as well as shoulders from VR to get that 2pc.
Aside from that, try to get the Vengeful Helm and the S3 axe, It's only 2200 arena points so 6-7 weeks should do it :)