Until I became a bit better at the game and had a fuller collection, I had a few go-to tactics against bosses:
- Get a first try with Abyssian swarm. Shadow Dancer wins you games because Boss AI doesn’t understand Deathwatch.
- Another option has been Magmar Grow decks. Specifically, if you can get Gargantuan Growth to stick on a minion, then you’re probably going to win.
For the longest time I also resorted to hiding behind Wood-Wen + Quartermaster Gauj or Sinister Silhouette, both are very good at confusing overwhelming Boss armies. As @alplod said, Sarlac is also confusing the boss AI.
Thunderhorn is a superb card that will be extremely valuable anyway, and that really help to turn the tides against minion-spamming Bosses.
Now that I have a larger collection, I found that an early game of Rescue RX, Biomimetic Hulk and assorted heals also help contain the more aggressive Boss starts.
Various Trial and Destiny decks are now extremely valid against Bosses, but they are not budget-friendly.