1) Iron Legacy
This fight is over in 4 rounds, win or lose, so no slow-build characters. That means Argent Adept and Absolute Zero are poor selections. Ongoing destruction is absolutely necessary, and ideally all 5 decks have some. IL will do lots of damage, so Omnitron-X can't maintain Components and is a poor choice, unless you pray for a melee damage reduction to open with. Damage Redirection is a great choice. You need to overcome damage reduction, so Legacy is a good choice to help everyone else. Characters with big One-shots (Ra, Tempest) do well. Damage Reduction and Healing work, which spells Nightmist, but I have not tried her on him.
2) The Matriarch
Damage reduction works nicely. This deck does a lot of 1 and 2 hits. Bunker, Legacy, Tempest are great. Wraith is great for manipulating the villain deck and damage reduction on Matriarch. Visionary is great for TTE on Matriarch. Nightmist is a survivor in this fight, but doesn't do much damage. Sudden Mana (Haka) Huginn and Muninn, Domains, and the Mask, but no more than that. Too many fowl under SM means Matriarch plays Ongoing destruction too fast to deal with, then SM is gone. Legacy for NE and LFTF are a definite plus. Tachyon is actually a very good choice, despite Nemesis penalty.
3) The Chairman
Haka to Sudden Mana all of the Thugs, then the Underbosses after Chairman flips. Legacy for LFTF and NE. Again, lots of small damage from this deck, so damage reduction is highly desired. Ongoing destruction doe snot come from one-shots, so SM is safe.
4) Kaargra Warfang
I have no standard for beating this deck, yet, but my current philosophy is to concentrate on generating favor fast on damage instead of destruction of targets or grabbing Titles. Wraith is self-supporting and can pop out 2 favor per round by Turn 2 often, or can churn away Fickle fans to protect favor. Haka is self-supporting, and can rampage a lot of favor. Legacy boosts a lot of 3 damage single target powers to 4 (Bunker, Ra, Naturalist, Fanatic), and 1 damage multi-target powers to 2 (Tempest), to help others produce favor. With good card draw, you can win Turn 3, but you want to go for reliable favor. If you take Haka, then cherry pick the villains that generate a lot of favor for Sudden Mana, but don't take all gladiators or you'll see Fickle fans spoiling the game.