I'd like to share my own method which involved very easy to obtain, cageable pets.
My goal was to avoid use of any pets that required a lot of work or randomization to get ahold of. IE, a lot of strategies use our Mechanical Gnome buddy which is a rare archeology find, and while I have one, many of my guildmates and friends who I'm trying to lure to pet battling, don't. So I mixed and matched strategies from other folks, and added a little of my own spice, and came up with this. It uses 3 very easily obtainable pets. Darkmoon Zepplin, easily purchaseable after 2 decent darkmoon faire events. Mini Mindslayer, drops off the first boss in Ahn Quiraj, myself I must have 20 of these in the bank from farming Anubisath Idols to sell. And Pet Bombling, very easy to create Engineering pet that you can either make yourself, or easily found on the AH of my server for ~200g. You'll probably want to burn a stone on him, I haven't tested this with a green quality one.
So here's my setup
Mini Mindslayer (Mana Surge, Amplify Magic, Life Exchange)
Darkmoon Zepplin (Missile, Explode, Decoy)
Pet Bombling (Zap, Toxic Smoke, Explode)
Open with Mini Mindlasyer
Use Life Exchange to knock out over 600hp from Lil Oondasta
He'll use frill blast and force your pet bombling out
Use Toxic Smoke
Use Toxic Smoke again
Bring out Darkmoon Zepplin
This strat has worked super well for me. None of the used moves rely on RNG, and the strat itself minimizes the effect of RNG, as both mechanicals have the self rez available. I have yet to fail using this team.