I felt they made this fight a little too easy by giving you those Vengeful Spirit cards, so I decided to beat the boss without them! It was a bit of a challenge, but after a few attempts I was successful!
How to win:
1. Mulligan hard for Depth Charge (it's better than doomsayer because of the dumb AI)
2. Play Depth Charge turn 2 (never turn 1)
Also, if you don't want the extra challenge, you can just use the Vengeful Spirits anyway to get an easy win :)