Well yeah, Deadline likes to destroy the environment deck, I haven't played him yet myself though, how often does that happen? Is he flipping every couple turns? or does it often take awhile? Do the heroes usually die before he ever gets that far?
What about on advanced?
And somewhat facetiously, has he ever destroyed a particularly annoying environment, and everyone just went "yay, thank goodness that place is destroyed. Good job Deadline!" (Like Rook City or something)
On average, he destroys a bit over 3 environment cards every 2 turns. The environment deck has 15 cards. That gives you a bit under 10 rounds to defeat him.
"Deja-fu? You've heard of that?"
- Lu Tze, Sweeper, Thief of Time by Terry Pratchett
Yeah, unless you have really reliable ongoing destruction, he flips about every other round. Your best bet will be to hit him as hard as you can, as much as you can.
We never look at the environment cards he removed, which introduces a lot of uncertainty...you can't bank on the environment doing things, but sometimes the environment doesn't do its nastiest things!
When he builds up a certain number (3, irrc) of special Ongings (cataclysms, iirc), he flips, destroys the ongoings to deal damage and removes environment cards from the game. Then, as long as another cataclysm isn't played that turn somehow, he flips back the next turn.
He tends to throw out cataclysms pretty quickly, so AZ is actually pretty good against Deadline for both the self-healing and his card that destroys up to 3 ongoings for damage.
This all changing in advanced mode, of course. Destroying his cataclysms becomes too painful, unless you have some kind of damage nullifier up.