The basic game plan here is to get the quest online as fast as possible, then use Augmented Elekk, Persistent Peddler, and Glide to fill your deck and cycle like crazy. As of the time that I'm writing this, Tradeable cards retain their cost reductions even when they get shuffled into the deck via means other than the Trade mechanic. So, over time you should end up with tons of 0-cost Persistent Peddlers (which is great for Spam Caller). Also, as of the timing I'm writing this, discounting a 0-cost card with the Demonslayer Kurtrus effect still counts as 2 mana for Vengeance Doesn't Come Cheap even though you can't technically reduce the cost beyond 0, so trading over and over makes a lot of progress against the achievement.

Finally, this includes one Lion's Frenzy along with some attack buffs for whenever you reach the end of the game and have nothing but card draw and tradeable cards. which can easily get this to 10 damage for Drawing Frenzy (note: you don't need the weapon to have 10 attack, you just need to deal at least 10 damage with the weapon, so Fury and Chaos Strike count).