The P.U.N.K engine is extremely synergistic with Archfiends, who are graveyard focused, have a lot of level 3s and 8s, and possess some strong recursion and backrow capabilities. Two of the centerpice monsters used by P.U.N.Ks, The Zombie Vampire and Psychic End Punisher, are also monsters Archfiends want to run for their gameplan, so the base gameplan for P.U.N.Ks also advances the Archfiend gameplan.
When going first, the ideal goal is to make Masterking and go through the P.U.N.K play sequence to make the Zombie Vampire and one or more of Chaos Angel, Baronne, and/or Hope Harbringer. Foxy Tune discards by effect, triggering Heiress and getting a boy on the board, the 600 LP cost of the psychic P.U.N.Ks allows Masterking to mill Tour Guide or Infernal Prodigy, and synergizes with the field spell, and tributing the Fusion can make A Deal With Dark Ruler live, enabling for Rank 8 plays. If you don't have the P.U.N.K pieces in your opening hand, you can still make a Chaos Angel if you have Infernal Prodigy + Archfiend Emperor/Diabolica, or if your Ze Amin gets Imperm'd/Ash'd, it and Garbage Lord can make Jam Dragon.
If you go 2nd, you want to aim for an OTK using Psychic End Punisher and/or Chaos Archfiend, but even Berserk Dragon can do the job. This is also where cards like Garbage Lord show additional utility, adding a body and making the OTK eaiser.
For fiends that you can mill for 600 LP, other good choices are Red Resonator, Sangan, or even Snipe Hunter, and Cherubini fits the deck as well.