Little Tommy Newcomer

Do not underestimate this little boy. His pet? Lil' Oondasta, the pet equivalent of the real Oondasta. It will hurt. But it is beatable.

How? You'll have to exploit pet abilities here. Mechanical pets will resist 2/3 of Lil' Oondasta's attacks, they can resurrect if they fall, and their attacks are strong against the beast-type foe. This means a mechanical pet can survive for around 2-4 turns. Magic pets also work well, as they will take a maximum of 35% of their max health in a hit, so it will take a minimum of 3 turns to kill them.

But even with a full team of mechanical and magic pets, don't expect this to be easy. You'll need some serious team synergy here to pull kill Lil' Oon before it kills you. As an example, here's my team:

Tranquil Mechanical Yeti
Key skills: Call Lightning
Note: Anything with Call Lightning will work most of the time with this strat. Mechanicals with it make it almost impossible for this strat to fail, even facing crits from Lil' Oondasta. If you can't get this, another fine choice is the Sunreaver Micro Sentry.

Clockwork Mechanical Gnome
Key skills: Build Turret, Metal Fist

Jade Oozeling
Key skills: Corrosion, Acidic Goo
Note: Check the breed of the Oozeling to make sure it has less health than the gnome. Otherwise this strat won't work. Thanks to the replies for pointing this out.

Turn 1, send out Yeti, use Call Lightning (all mechanical attacks do more damage, all attacks add an extra lightning strike). Oon will blast Yeti, sending it to the back row.

Turn 2-5, use Gnome to set up two turrets and use Metal Fist in between. The turrets deal damage three times each round each, so that's three lightning strikes per round. Each turret set up gets a total of 12 bonus lightning strikes. Gnome will likely be killed for good after turn 5.

Turn 6: Jade Oozeling sent out, use Corrosion to increase the damage of all attacks against Lil' Oon. The two turrets up will then hit a total of six times, followed by six lightning strikes, all amplified by the Corrosion. If Lil' Oon is still up, use Acidic Goo to do even more damage.

There's a bit of variation with this strat, depending on whether Lil' Oon's attacks hit, crit, or miss, but it's quite resilient. If the Gnome lives an extra turn, throw in another Metal Fist. If the Gnome dies early, just use Corrosion and then Acidic Goo with the Oozeling, and then Call Lightning again when the Yeti comes back out.

Used
Clockwork Gnome S/B 1,1,1
Zandarlari Kneebiter S/S 2,2,2
Zandarlari Kneebiter P/B 2/2/2

Round 1: Build Turret
Round 2: Black Claw
Round 3: Hunting Party

if you die

Round 4: Hunting Party with second kneebiter

Here's how I beat him

Team: Wild Golden Hatchling, Clockwork Gnome, Cogblade Raptor

I started with gold hatchling and used call lightning, then got killed by frill blast, which brought out my clock work gnome

I built a turret, then used metal fist until he killed me.

Cogblade raptor comes in, Expose Wounds, so the turret and lightning storm do some nasty damage, and finish him with batter.