No healers and healing is reduced.
Hero selection: Damage heroes only
Yep, the challenge says no healers but tanks aren't allowed meaning no shields aside from Symmetra's ult. This sounds like a problem but really, with some map knowledge and abusing stairs, which we'll get to later, this challenge isn't all that bad. Now, onto who we beat it with and what my opinions are on the setup.
Bastion, McCree, Torbjorn, Reaper. Now you'd think Reaper would be a good choice but in reality he isn't, and Torb's turret is actually useless in terms of healing. It doesn't do any making him a beefy character who can't do much for self-healing. Bastion and McCree are both great characters still considering the HPS of Bastion and McCree's ult and stun.
Soldier and Symmetra are both characters that personally I feel will help out despite the healing reduction on Soldier. Symmetra's ult is the closest thing you can get to a shield in this mode so use it wisely if you decide to play her. Haven't tested Ashe, Junkrat, or Hanzo but I'm sure they're all viable here aswell.
What this map really comes down to, especially in the castle, is awareness and map knowledge. You NEED to abuse the staircase on the left when you enter and retreat through the hole in the wall and make ypur way around. If someone dies you have plenty of time. Kill the first heavy ASAP because if you don't even the Bastion's damage won't be able to help you. My team, who has done every archive mission flawless had a couple close calls where only 1 of us was alive so don't think because you can heal doing damage that it'll be easy, Bastion can't even out-heal the heavies damage and getting charged by one will most likely mean the death for him. Communicate with your team, stay as far away from the special enemies as possible and you'll make it. The hardest part is the castle with the 2 heavies but making sure you kill the first before the second drops will make it much much easier.
My teams setup:
Bastion, McCree, Reaper, Torbjorn.