Mulligans
General Mulligans
Draw and control.
Aggro Mulligans
Control the board until you can draw Supreme Archaeology and plot twist away.
Control Mulligans
You'll need Impbalming to destroy big stuff like giants, but otherwise you're pretty chill. Draw cards and reshuffle until you get your quest done, at which point you can replace your deck with Legendaries.
Draw a lot of cards and try your best to control the board. Clear big minions with Impbalming, small boards with Shriek and Hellfire, and reshufle your hand with Plot Twist. Heal with Aranasi when you do, and Betrug in combination with Plot Twist will summon a ton of minions to your board and allow you to do crazy boardclears using Burly Shovelfist and Deranged Doctor, healing for a ton as well.
Possible drops: Loot Hoarder, Mortal Coil, Big Bad Archmage. Depends on how good other support is