Try to do this with a team that has some strong healing and/or mitigation AND while leveling. You will still need ton of switching and really good luck. Crawdad is not exactly one easily obtainable pet, though... I would go with Anubisath Idol
(lvl 10), Emerald Proto-Whelp
(at least lvl 20), S/S Rabbit
(lvl 15), Spawn of Onyxia
(10), Strand Crab
/Crawler (10), Scourged Whelpling
(15) but im sure there are many more. Basically each pet should have at least two avoidance / HoT / shield type / heal abilities.
TBH, I am pretty glad I got it in one of last days of 5.1 before the huge pet balance changes with Lil Rag, FFF and Anubisath Idol. Still, the counter stopped at four several times.
Also a note: do not do PvE battles between PvP, they seem to be resetting the counter - at least that what was happening to me and I was wondering why havent I received the achievement already... Then I figured out I was doing PvE, too (without deaths)