Objective: Escape Vorkuta
Step 1: Secure the Keys
Watch the scenes and once prompted, hit the guard.
Step 2: Ascend from darkness
Step 3: Rain fire
Run along the tunnels and kill any guards that will stop you along the way. Ride the elevator with the others. Pick up the Makarov from the fallen soldier and wait for the mg fodder to open the door. Once open, sprint and duck behind the mining cart to avoid getting chewed up by the MG. Stay behind the cart and take care of the soldiers on both sides. After stopping a bit, wait for the other prisoners to blow up the tower ahead and open the gate. Follow Reznov.
Step 4: Unleash the horde
Follow Reznov to the building. Go upstairs and find the intel on the shelf, near the comms.
Vorkuta Intel 1/3
Continue upstairs and man the slingshot. You need to destroy the three targets. You can unlock the achievement, 'Slingshot Kid' by destroying three targets without missing. The trick here is to pull the slingshot all the way back, make sure the bottom point of the crosshair is aligned and over to the yellow dot on the target's name. Refer to the video below to know more. If you missed, you can just Save and Quit, then resume the game to try again.
Slingshot Kid achievement
Step 5: Skewer the winged beast
After destroying the targets, rendezvous with Reznov and grab yourself a shotgun. Shoot the locks and kill the two soldiers nearby. Grab their AK's then take the alley to the right. Shoot the RPG soldier on the roof. More soldiers will arrive so get rid of them. Move behind the buildings to reach the next building. Go upstairs and grab the harpoon. Shoot the helicopter to bring it down.
Get to the Armory
Step 6: Wield a fist of Iron
Go downstairs and head to the next building. Grab the Ak with Grenade Launcher near the entrance and use it to effectively take out the enemies behind cover. Clear the next hallway, go upstairs and do the same. The door will start to close but Sergei will stop it for you. Slide under and head to the next room. Open the door so your allies can assist you, then check the dark room beside the stairs for another intel. Check the video below for further reference.
Vorkuta Intel 2/3
After that, go upstairs and follow Reznov to the annex. There will be heavily armed guards that will breach in so ready your shotgun to take them out easily. Take out more guards and follow Reznov as he attempts to open the vault door. Stay nearby and take out enemies as they come. Once Reznov opens the vault, go inside and grab the Mini-gun.
Step 7: Raise hell
Go through the opening on the wall and go outside. Advance and sweep the area for enemies. You should have more than enough ammo until you reach the next objective.
Step: 8: Freedom
Once you've regained consciousness, don't ride the bike yet. The mission's last intel is located in one of the racks behind Reznov.
Vorkuta Intel 3/3
Ride the bike and make your escape. Shoot all targets along the way until you get the prompt to commandeer an mg truck. Use the mg to take out as many enemies as you can. You'll finally get the chance to jump off to the train and complete the mission.
This 'mission' is just a whole long scene let's just skip to the next one.