Flying Brawler

Tried the Moth setup. I won like 1 out of 8.. it did not work at all for me.
So I decided to try my own setup, I used:

[npc=63098] 1, 2, 1 skills, breed: B/B

[npc=115787] 2, 1, 1 skills, breed: P/S

[npc=115785] 1, 2, 1 skills, breed: H/P

I am still trying this, but so far I am 3 out of 3 wins.

Start with [npc=63098]. Use your pets logically, wait for other guy to put his weather, then [pet-ability=256] to counter, and [pet-ability=517] and so on.
Use [pet-ability=112] as filler.

So far I beat most teams with just the [npc=63098], but the other two are ferocious as well, so you have proper backup.

Anyways, this worked for me so far, a lot better than moth.
I hope this helps, good luck and happy hunting. :)

I have had good luck with Chi-Chi, Teroclaw Hatchling, and Sentinel's Companion. Use healing moves (tranquility and Nature's Ward) and dodge abilities (Ethereal and Dodge). My exact move set is
Chi-Chi- 1,1,1
Teroclaw- 2,2,2
Sentinel's Companion- 2,2,1

Three moths rock this achievement. I chose to use three with Reckless Strike (+ Cocoon Strike and Moth Dust) and doing the usual mindless RS-CS-RS-MD-RS-CS-RS-MD- etc etc spam. Very strong all-round team, but of course cannot conquer all. When the sleep hits, it is a home-run (but it rarely does and the strat does not depend on it either). It is also quite mindless and you can easily do other stuff on the side.

[npc=88422] (P/S) 2/1/1
[npc=73368] (P/S) 2/1/1
[npc=97547] (P/P) 2/1/1

I fled from mech-heavy decoy teams and dragon-heavy (curse you, Emerald Dream!) teams and for the rest it was 10 wins out of 13 fights - lost to a Teroclaw Hatchling team and an Imp/Crusher team and got pwned by a very lucky Magma Trap team!

A more cautious person might pick Alpha Strike instead of Reckless Strike and might also bring a moth with Moth Balls instead of Moth Dust to counter those decoys, but I am not sure it is as effective against random teams.