I actually got this fairly easily by being somewhat cheap. It made me feel a little bad for the people I fought, but it was only five matches, and it is what it is *Shrug*... Anyway...
What I did was I made a team using my Panda Cub (who I think was about level 15-16 at the time) and 2 level 1 pets. Really didn't matter what they were.
The matchmaking system would average out the teams, and always place me against someone who had three pets in the level 7-10ish range. And a level 15 Panda Cub can fairly easily whup three level 7-10ish pets. The level 1 pets never even came into play, they were just there to break the curve... so to speak. It's not hard for many pets to beat 3 pets half their level.
So yeah, my Panda steamrolled 5 battles, I got the achievement, and then I started playing fair again, lol...
Now, I did this in week one, where tons of people were still pet battling so the queues were pretty fast. Try it now and you may be in for a wait. Pet battles seem to have died down a bit, all my queues have been longer of late, especially at oddball levels. But worth a shot if you have the patience.
BTW, highly recommend the Panda Cub as a tanking pet. He's not that great at lower levels, but gets unstoppable in mid to high levels. I use Roar, Hibernate and Maul as my build. Using Maul with the buff from Roar does huge damage. I frequently 2-Shot same-level pets with the combo. (It's really more a 1-Shot with Maul, but you need that first roar to apply the buff, lol). He takes minimal damage, lots of HP. And can reliably heal to full or nearly full with his hibernate ability. While he's hibernating, the cooldown on Maul ticks off, making it useable again as soon as he wakes up. Plus he's a beast, so he's great for stomping the hundreds of critters you run into in wild battles, which consequently also makes him easy to level. And he's not bad at stomping non-critter types either. He's totally the backbone of any team I make, lol.
Since the Panda Cub isn't exactly common or easy to come by, I believe the Hyjal Cub and Baby Blizzard Bear have most or all of the same abilities, just mixed up slightly so you get them at different levels. Possibly other bear cubs as well.