Listen to the Russian chatter and marvel at the lengths they went to here to make sure things were realistic. Sounds great and it stays in Russian... through the entire mission. That's great and all but it means you really need to keep your wits about you because, unless you understand Russian, you are going to have to be reading subtitles to be told of the enemy flanking you. Thankfully there aren't really many opportunities for that.
Once you are out of the car, stay in cover and keep moving. You'll head lower into the parking garage. If you hug any of the pillars in the garage areas, they will provide you with plenty of cover. But you need to be right up on top of it. This holds true for most of the mission. Move from pillar to pillar and let your squad deal with most of the enemies. This is another one of those missions again. Go through the back of the area to the elevators and go down a level. Take cover behind the white vans on the left side and take out enemies through the gap in between them. Head up the left side of the room when you are done and go down another level.
I recommend going up the left side behind your teammate and then using the cars on the left for cover but move slowly. You want to only have to use any one car for a split second before moving to something sturdier so that you don't blow up. Wrap around the corner and use the van for cover here. Continue clearing and moving up the left side. Climb up the ramp on the far side. Follow your squad through some halls and you'll breach a room. They'll get most of the guys in the room but there will still be one for you. You'll get a QTE to put on a gas mask. Move through the room and up the stairs and at the top you'll have another QTE.
Go through the door and down the hall into a larger open area. When you can, stay right and use solid walls for cover. From here you should be provided with a large number of flanking opportunities. Move through here and you'll come to a much more open area. Stick to the wall on the right side and try to help clear the area (or just let your team do so). The only person to be concerned with is an enemy with an LMG on the balcony at the far end. Unfortunately, YOU have to take him out because your team won't. Kill him and then follow your team up some stairs.
You'll enter another area similar to the red room open area downstairs. Stick to the right again but be careful because the cover isn't as good here and there are more enemies. You'll get to a rather open area after this. Try and clear it from cover but you can also move up the left side and to the open doors in the back without clearing the area. You'll hit a checkpoint and cinematic on the other side which will prevent you from being killed. Breach the door and you'll enter a rather hectic area.
In this area, start by heading left and staying low. Clear enemies in each station as you go and move to the next row. Move to the right side and stay on the right side this time. Move around the right back most station while prone and slowly weed out the enemies that come towards you. Go through the door they were coming from and follow your squad and you'll get another QTE.
Head through the door at the end and you'll get to the bank lobby. You want to get to the front door of the lobby and move up behind your squad by the pillar. Try to pass them. Wait until they move forward and move up behind them. Then you'll want to move to the far right corner of the plaza. Yes, you want to shoot the cops here. Move through the cars on the street to a bus, clearing as you go. Go around the back of the bus and get in cover on the left side of the street. Kill some of the cops here but watch for three SWAT members who will be coming up the middle of the street. You want to kill them quickly, they are very dangerous. Go up the hill and follow your squad. Dodge!
Continue chasing after the guy and ignore everything else. You'll have to run through bullets (which can kill you) while trying to catch him. Once you've reached the train station, you'll get a QTE. Take the guy out and inspect the bomb to finish the mission. If you managed to make it here from the bank in under 2:40, you'll get a chievo/trophy.
