Old Wounds

Right at the start, you'll see a body near where you spawn. Interact with it to pick up the pulwar sword. Just go around and use it to get 15 melee kills on enemies throughout the mission. Easy peasy.

You'll find mortars in a cave inside the base, shortly after meeting your contact. Grab them, and head out through the gate. Keep an eye out for a helicopter taking off – hit it twice with a thrown mortar to take it down and complete this challenge.

In the first area you need to defend, there's an unlockable chest with anti-tank mines. It's up high on a ruined structure near where you find stingers. Once you're back in the main defense area and tanks show up, get off your horse, plant a mine in front of one, and boom! Challenge complete.

This one's pretty straightforward. Just ride your horse into 10 enemy soldiers. Keep an eye out for groups and just charge 'em.

Near the base entrance, there's a truck with a mounted MG. Around the middle of the mission, a bunch of helicopters will show up to attack. Hop onto that truck turret and take down one of those choppers. You'll get this challenge done in no time.

After you destroy the arch, head back to the main area in front of the base and take a left. After a short ride, you'll see four enemy helicopters. Take all of them down using your stinger. This is also a good spot for the next challenge.

This is done in the same spot as the previous challenge. After destroying the arch, go back to the main area and turn left. When the helicopters appear, use your stinger but don't use the lock-on feature. Just aim and fire. Since they're dropping troops and tend to hover, it's easier to get this done here without locking on.