This was really cool! I went for the middle satan, messed it up first time but got it second. Super satisfying to play! The medusa like thingy was really powerful, and I based my main deck around them. Though, in preparation for the battle against satan I stocked up on the 17 point self sacrificing ones.
A note of feedback though; currently there is no incentive to restart other than "I want to fuckin summon satan". Into the breach has a great mechanic, when you lose, you get to pick one of your units to bring along to your next run. It gives you a bit more of a reason to start another run, and honestly selecting a unit to bring along just feels better than clicking a restart button.
Edit: bonus note; steam users seem to like demos, and you have a playable game that could work really well as that. Could be worth thinking about.
Also, the music is incredible, and I adore the visuals. Fantastic work!