Update: This can be done in the DLC.
(I also need to heavily update the solution below.)
"Challenge mode" is a difficulty that's above "Hard" and you unlock it once you hit level 30. You can presumably only select it on stages you have completed on Normal difficulty previously.
Here are some other things that have been brought to my attention.
-The map you play doesn't need to be a "Daily"
-The map you play on Challenge won't count towards the missions you have to play on Hard
-Bonus armor destruction and special ammo can be very helpful
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Have everyone in your group stack Smart Cover with the Recharge Skill mod, you'll basically be invincibleThe last one is very important, makes things a lot easier.
The most common stage played to get this achievement done is "Lincoln Tunnel Checkpoint". It's pretty short and straight forward, enemies don't pop up behind you or anything.
Here are two videos of people running through the stage:
I put Maka's guide first because he gives tips while playing and that should be sufficient.
Admittedly it's not that hard as long as you're prepped with proper gear and weapons. Most if not all of your stuff should be purple or gear that is level 28+.
Your playstyle and what you bring can be very flexible but two people at the least should bring some type of healing abilities, anything that can get you more ammo can be useful and more importantly than anything else actually in game is patience.
You'll mostly be sitting back just filling enemies with bullets. Then later in the stage you'll be jumping around like crazy to avoid nades when you get to the final boss waves.
You're allowed to have your team get wiped, no one will respawn but you will reload the last check point.
If you some how managed to get to level 30 without knowing you can revive people that die well you can, it just takes longer than a revive on a downed person does and the dead person can't move to a safe place for you to revive them.
I don't know if the amount of players in your party effects the stats of enemies but it will not effect the amount of enemies.
This can take anywhere from as little as twenty minutes and as long as over an hour depending on both luck and skill.
If your game crashes and you're not host you can simply reboot the game and signing back in with your character should rejoin the match and you will still unlock it. If something happens to the host the party will be disbanded and you'll probably have to restart or if servers go down for any reason you'll definitely have to restart.
All in all it's not too bad, just takes time. Good luck.