I beat her very repeatably with:
Death Adder [S/S] 1,1,2
Fel Flame [H/P] 1,1,1
Lil Bling[*] 1,2,1
It's not a fast strat, but the key is the Death Adder neuters most of the first pet and then uses lightning storm against the mech.
Poison Fang -> Blinding Poison -> Puncture Wound -> Poison Fang
Rotating this 3x ended up in him only hitting the Death Adder twice and none of his AoE attacks hitting. Once he dies, the mech starts up and you just cast Poison Fang, which kinda uses Call Lightning against him. After that, The Fel flame kills him in 2 hits (immolate, conflagrate). This is the only awkward part of the strat. I didn't do well bringing in Lil' Bling at this point, even though Lightning storm should be helpful. So I just rode out 2 or 3 of the last 3 rounds of lightning storm with my elemental and took the hits from the wolf till my elemental died. Then I just started with extra plating (usually the wolf was in prowl), followed by Make it rain and and smack that. If the wolf was dodging, I made sure to refresh make it rain one of the dodging turns.
If I had to change anything on the strat, I would replace Lil' bling with something different, but I didn't spend enough time to figure out what worked better since it consistently beat the battle multiple times. I really liked how the Death Adder did against the first (and partially the second) pets.
Carry Pet Experience Reference Guide: