Overwatch 2

I would like to note that I was in TheBigTicket94 's group as the Moira. I decided to have a written explanation as well as add my perceptive. If you want to see McCree's POV, go see his solution.

[Edit]: Epilepsy Sucks has informed me of methods that his group used to deal with the Heavy Assaults. They have been added and you can choose which one you think your team will work better with.

Enemies

Part 1: Breaching the Door
This section consists of 3 waves of enemies. Enemies will start to spawn on either sides of the door, in which case the siren above the door will light up and start blaring, or through the ceiling, in which case someone will call out the enemies, glass will shatter, and troopers will drop in the center.
If enemies come from the the side doors, more enemies will spawn on to the rooms beside of the doors. If enemies come from the ceiling, enemies will spawn in the room behind you.
When you clear all 3 waves, the door will open and you can proceed.

Part 2: Pre-Sniper Road
A small section with some enemies to your left and right. At this point, Reyes (Reaper) should teleport to the sniper's location.
When you clear all of the enemies, the sniper will spawn in with a cutscene.

Part 3: Sniper
Another small section. Reyes should be up with the sniper and take her out with relative ease. Genji and McCree should take out the enemies that spawn across the exploded door and Moira should be healing the two on the ground.
When you reach the docks, the next enemies will spawn.

Part 4: The Docks
Dropships will come in with tons of Enforcers. Moira should use Coalescence as soon as the Enforcers touch the ground to take them out and heal allies at the same time.
Next, ships will come to the docks. McCree should use Deadeye to take all of the enemies on the boat and the Sniper.
Enemies will come out the door to the left. This is the door you want to go into.

Part 5: Hotel Room
3 Troopers will crash in from the two side windows and the door. Some more will run up top. The door in the middle occasionally stay intact. If this happens, it will create an "invisible wall" of sorts that won't allow you to shot through it (although the enemies can still shot you). Also the doors aren't solid, but still block your view. It's a really annoying glitch and you can see it clearly in TheBigTicket94's video.
The next wave will spawn once you step outside.

Part 6: Sniper Bridge
A sniper will spawn as well as some troopers and enforcers. Moira should throw healing orbs and keep everyone topped off. Reyes should kill enemies that come inside. Genji should try and deflect the sniper's shot and McCree can try and help both Reyes and Genji.
The next wave spawns when you reach the courtyard. Reyes and McCree should stay behind, across the bridge, Moira should be on the bridge to take care of Genji, and Genji should trigger the assassin.

Part 7: Assassin's Courtyard
Run back to McCree and Reyes. The assassin will usually attack from the bridge or from the right. You should all focus her down, including meleeing whoever she pins. Some more enemies will come across the bridge. Clear them. McCree and Genji should go across the bridge, under arch, and take the stairs to the left to the high ground.
Reyes and Moira should move forward to spawn the next wave.

Part 8: Heavy Assault (HA) Bridge
Moira and Reyes should return to the other two. Moira should stay with the Genji and McCree while Reyes should make sure not enemies come up the stairs. McCree should Deadeye and Moira should make sure he stays alive. When the HA is near the stairs, run back to the very first Sniper's position (the one that had the cutscene). Deal damage to the HA and if you need to, return to your original position near the courtyard/bridge, although be careful as enemies are constantly spawning, so some will be in your way. Keep doing this until the HA is dead.
Go into the the door across the HA's bridge, into the art gallery. If you want to charge your ultimates here, you can as enemies infinitely spawn.
Step into the center of the art gallery to spawn the next wave.

Part 9: Art Gallery
You should stay near the door and McCree should Deadeye to take care of the enemies who drop down. An assassins will spawn, so just deal with it like the one earlier.
Walk through the door across the art gallery. It will shut behind you when all 4 players enter.

Part 10: Extraction Point
There is a raised platform in from of you, the roof, that has chairs and silverware on it. It is essential that you clear the tables and knock off chairs. Trust me.
Once you've done that, there's a room to the back left. Everyone should head there. Moira should stay in the corner away from the water, but close to the door and send her healing orbs in front of her so that it can heal everyone. She should try and not use all her primary healing all together, since she won't be attacking, but save it for when people are low or are expected to take damage. The other three should be killing everything outside.
For Snipers, you should try and only peek in between shots. Genji should try and deflect while McCree uses Deadeye behind him and Moira heals both of them.
For Assassin's you should melee her ASAP and just pump damage into her.
There are three waves with one boss in the first wave and two in the second. They are randomly Assassins and Snipers.

For the third wave, move to the balcony above the art gallery door. A Sniper will spawn, which should be taken out/damaged with Deadeye. The HA will drop on the roof or on the floor between the kitchen (which is below the roof) and the art gallery door. You should try and bait it to move up while damaging it. When it does move up, drop down. When it drops down, move up. Rinse and repeat. Reyes should be clean up the smaller enemies.
Once the HA is dead, everyone should move to the roof and wait for the ship. Enemies will still spawn and can kill you, so enter the ship as soon as it open up.

Video of Moldy Tacos5000, ReachDragon, TheBigTicket94, and I
If you have any Moira specific questions, I'd be happy to answer them.

Here is a video of me and some friends beating Expert with no deaths.

Hope it helps out. Thanks for watching!

Slow and steady wins this one. Here are some of the key things you should do to make this easy (see the first video below for the time stamps)

First Assassin - Assassin's Courtyard (8:00)
Use the couch at the back of the house to easily take care of the assassin. Right after you kill her, run back outside the house and let the enemies pile through the door. Moira or Reapers ult should be able to get rid of most, if not all of the enemies.

The First Heavy Assault (9:45)
Use the building to your advantage. Keep going around the building and using the stairs as needed to kite the heavy assault. Slow, steady and patience will be the key for this. Dont over commit, and play it safe, and you should be able to get the kill relatively easy.

Second Assassin - Art Gallery (17:55)
Make sure everyone has their ults to make this easy. Have Reaper go the center and use his utl. If you want, McCree can also use his ult to clear more ads. Moira should be healing Reaper/McCree either through regular heals or through her ult. Once the enemies are cleared, take care of the assassin as soon as possible. Genji should utl the assassin for an easy kill.

Extraction Point - Wave 1 & Wave 2 (18:50)
Use the room in the far back left of the map to get through the 2 waves. They will be a random combination of Snipers and Assassins. Just keep your cool and play it slow and you should be able to get through this portion fairly easy.

Extraction Point - Heavy Assault (23:40)
The best way to beat this is to kite the Heavy Assault along the map. If you play a lot of COD Zombies, then the same principle applies, just control where the Heavy Assault walks and you should be able to chip its life little by little. Go to the videos below to see the route we took to kill the Heavy Assault. Ideally, McCree and Reaper should be killing ads, while Genji will be doing most of the damage from deflect. Moira should be healing most of the time and only damage the Heavy Assault when she has her ult.

Good luck to everyone and hopefully this helps out. I posted the videos of both my clears with two different teams. Both are from Moira's point of view.

First Clear
Genji - FrozenImplosion
Reaper - Kuya AJ
McCree - Doc Showtime
Moira - Tekmote
Second Clear
Genji - USG AESOP SL
Reaper - AngloSaxton
McCree - Clutch Rino
Moira - Tekmote
Third Clear
Genji - The SCHWARTZ 00
Reaper - King Cadow
McCree - Unmet Player
Moira - Tekmote
Fourth Clear
Moira - Tekmote
McCree - A BAD SNIP3R
Genji - Eschultzy27
Reaper - hockey529