i've completed Deadly with an Escher gang of 5 Tier 3 completion. 400 health is a thing, most of your damage will come from crits as everything else is graze. Here are the things i needed to accomplish it.
Rank V armor and weapons required. take all their rank VI weapons as soon as possible in order to reduce their damage potential in future conflicts. (never did find any rank VI armor, but i've got most weapons of rank VI now)
No rushing ahead with any of the team until subsequent shifts where i've already stolen all their gear. Stay back, overwatch, and to a lesser extent ambush (this can pull you out of position and then get squished).
You have to use terrain to block LoS and try and force the other gangs to fight each other before you jump in (i faced all 3 other gangs in most shifts i played). Choose your starting location carefully for this reason, being out of the fight for 1 round is much better than the match being over for you after 2 rounds...
Everyone carries Adrenaline shot and a heal consumable. don't rush to revive guys, wait until you can ensure they don't just get spiked back down (and beware expecting to use Stinger Mould on revived guys, for some reason it treats them like they're engaged and won't allow use of heals).
Deadeye Leader with Heroic Barrage was my damage output (Autogun > Lasgun > Plasma). Brawlers with Heavy clubs are great (chainsword/power sword and power maul is better but 2h weapons are more fun although they can get screwed over by some of the buffs and debuffs at this level), my Mechanic was also Melee (rock drill and sword/axe depending on mood). Heavy ran Autocannon or Stubber (stubber > autocannon > plasma cannon > lascannon, but the range on the Autocannon can be very handy if your Heavy is crowd control instead of damage output, which is more needed at this point). Sab runs hand flamer and rank VI spud jacker i stole from someone, but mostly just throws Nades, Null, Halluc, and Chems. (Null Nades are super handy at this level...)
AI is dumb, so abuse it where you can. Strategy for them boggles my mind, but pretty much every opponent will be able to train you down in 1 turn, so don't let them.
Target Priority - Brawlers/Deadeyes, Heavies, Mechanics, Sabs - only Sabs won't be able to 1 turn kill your guys at this level. This can change depending on their loadout, if you've already stolen the Deadeyes' rank VI auto/lasgun they aren't as much of a problem as the Heavy with the rank VI stubber or the Mechanic with the rank VI rock drill and hydraulic slam...
Hope this helps. i'm playing on PC if it matters...