Mint, with all heroes standing. This one wasn't as bad for me as I'd heard about on the GTG forums. Naturalist had 6, Expat 11, KNYFE 7, and PWAA 9 HP, and that was with me making a mistake in round 2 that cost everyone an additional 2 HP. Oh well, it worked out OK.
It's hard to recommend specific things past the first couple of rounds since multiple cards of Deadline's cause deck shuffles, but in general, here's what happened...
Naturalist: As soon as I saw Calculated Orogenesis, I countered with Environmental Allies / Gazelle to at least save us from that damage. After Deadline flipped, I swapped to Croc and went full-out for damage. Predator's Eye came up on my last draw, and it helped us *easily* burst Deadline down from ~30 HP in the last round.
Expat: Never met a card she didn't like in this game. Liquid Nit Rounds actually didn't end up doing any good, but three guns (Pride/Prejudice/Assault Rifle) and two copies of Unload gave her consistent damage throughout the fight. Unload in the last round did a little bonus damage thanks to Predator's Eye. Two Flak Jackets didn't keep her alive, exactly, but they didn't hurt!
KNYFE: In the first couple rounds, I used her power, once on Naturalist, once on Argent Adept (after I'd previously stacked the bottom of his deck using Arcane Cadence; spoilers, I stacked it with another Arcane Cadence). I also tried using her power on Expat, but that didn't help. Maybe after the reshuffle it would have? But after that point, I was using Primed Punch every round to do 4 (or 6 if Predator's Eye was out) to Deadline. I blew up Primed Punch in the last round for extra damage.
PW Argent Adept: PW Argent Adept is best Argent Adept, if you ask me. He is my go-to character when I want shenanigans, and he gave me plenty of shenanigans. I started out by making sure I had Sarabande of Destruction out, thinking I would need to blow up Environment cards to keep myself alive... but after my dual Arcane Cadences, I realized he would be more valuable passing stuff around. So, off I went with the Lyra + Inspiring Supertonic + Inventive Preparation. Passing Expat the powers helped get Deadline's extra targets (and some environment targets) dead, or passing Naturalist the powers had him chomping Deadline for 4 damage a shot. Card plays typically went to Naturalist, though I also gave a couple to Expat, who finished the game with 0 cards in hand.
I also had an early Vernal Sonata that let me replay both Threatening Stomp and Energy Burn, both of which were super helpful.
My mistake was with Argent Adept - I blew up the wrong environment card in round 2. I'm not familiar with the MDP, and didn't remember that one of its cards would be playing more environment cards. Oh well, that extra damage from Deadline (and ourselves) wasn't fatal.
Environment: Total non-factor outside of Deadline using it to deal damage.
Deadline: I never destroyed any of his ongoings, prefering to just smack him around. I focus-fired the Auto-Armor Caster when it came out, but I ignored the Glaive, just letting Expat ping it down with the Assault Rifle while everyone else focused on Deadline. He flipped twice, destroying 5 environment cards the first time, and another 3 the second time.