When the mission begins, you're told to get on the horse, but go over to the "Access" point on your map to pry the Pulwar Sword from the dead body. Once you get that, get on the horse and keep following Zhao and Woods until you get to a camp. Dismount and follow them inside of the cave.
After the scene is over, you'll be attacked by some Russians, so run back outside and get on your horse again. You'll encounter some enemies on the way, so feel free to run them over, as you follow Zhao and Woods to the next area. As soon as you get there, you will be in a rather large firefight against the Russians. Progress slowly, picking off any in your way until you see some BTRs arriving.
Naturally, your assault rifle isn't going to do much damage to the BTR, so continue killing any enemies in your way as you move towards the weapons marker. Go up the stairs and grab the RPG, then blow up the two BTRs when you get clear shots. To ensure no more make it past this area, you're told to place a cratering charge at the entrance, so get over there and place it, then move to where Woods is so you can detonate it.
Make sure you keep the RPG, as you'll be needing it. Get back on your horse and head back to the camp, and on your way back, you'll run into some more heavy armor. Blow them up with the RPG and some enemy helis will attack the base. The RPG has an air-mode, so switch to it and take down all the copters that attack.
After the coast is clear, you will need to go and get back the weapons cache from the enemy. Start riding your horse to the marker, where you will be stopped and be under heavy fire. There are a good number of helis in the air, as well as an unlimited number of troops on the ground. To make matters worse, a BTR will eventually show up, too.
Your first priority is to take out the helis and the BTR when it appears. There's not much reason to kill the enemies on the ground, since they will just respawn, so find the ladder that leads up to the cache and clear the area of enemies. Just approach the cache and wait for your ally to get to it, which will trigger you capturing it. After that, you are told to get back to the base, where a scene will occur.
Once the scene is over, you'll charge forward on your horse (automatically) until it is shot and you're on the ground behind it. Hold both buttons on the screen to escape, then some scenes will occur. When you're in a cave doing some interrogating, you will be told to tap a button to resist shooting the prisoner. Keep tapping the button until you get enough information out of him, then Woods will shoot him. After some more scenes, the mission will be over.
