The 2nd boss Faerlina, I just used zoolock as many recommended and rolled through.
The 3rd boss Maexxa I used a modified cheap and incomplete version of freeze mage, no trap, no Blizzard. Main cards are Elven Archer and Bluegill Warrior to quickly kill the Haunted Creeper and fill her board so she cant summon big minions, Hex and Fireball for removal of big minions, Earthen Ring Farseer and Voodoo Doctor for much needed regeneration and arcane golem for constant damage output. And just fill the rest of the deck with whatever stalling spell i have. The key is to just ignore all the small minions she has, topdeck Voodoo Doctor and Earthen Ring Farseer early, and having timely removal whenever she has change to play big minions. A full board with 1 dmg minions will only hurts you 1hp per turn if you pull out double Earthen Ring Farseer early enough
Overall it's pretty challenging for budget deck but still doable