Bring an SOA ability or two. Draw one and you can manipulate the draws a little.
Play a GHEIST/Roots half or mono.
Play clans with their own attack/power manipulation. There are tonnes of cards that work well against him.
Any SOAability card with 6 or more power (then add bonus)
Any SOA bonus cards with 6 or more power (then add ability)
He's far from omnipotent.
If you're having trouble with Jungo, there are ways to tailor your deck to help.
Opponent usually does not start a round with Troompah, saving her for last. As most mentioned already, she loses out agains SoA. Also, high pill battles with at least 2-power difference (any 8 powered or something like Pilzken) can beat her at end-game if both sides have a large number of pills. DR don't seem to be as effective against her 9-life gap potential.
IMO Troompah is strong, but nowhere near as overpowered and other players make her seem. Artus does a good job of blocking her, but the idea is to pack some SoA without running a SoA clan ( so you wont be trapped to play SoA against Ashiko or something ). This week I'm running Junkz + Ulu Watu, high power wins out on Troompah with a few pillz, Qubik and Fuzz destroy her.