There are nine XOF unit patches. All of them are found within the Ground Zeroes main mission.

To earn credit for collecting any of the patches, you must finish the mission by extracting both Paz and Chico. If you happen to die before a checkpoint and you collected a few patches prior to reaching that checkpoint, you will need to collect the patches again. The achievement will unlock after gathering all nine patches once you complete the mission and get to the rewards screen after the cutscenes. You can skip the cutscenes if you've already seen them by pressing and choosing "skip."

Use night vision to help highlight the XOF patches if you're having trouble seeing them.

Pressing opens up a map of the camp. Make use of the compass there and direct yourself as needed.

Patch #1
From where you start the mission, turn around 180 degrees. Get to the edge of the cliff and move right, over to the bushes. The patch will be near there.

Patch #2
This is located in the same place where the prisoner is for the Rescue achievement. It's on the south-most side in this area, in front of the tents on a small pile of rock, sandbags, and garbage.

Patch #3
Head over to the cages where Chico is imprisoned and pick open the locked gate. The patch is on the ground directly in front of you, only a step or two from the gate.

Patch #4
From the previous patch, turn around and head over to the small shack/guard post. Climb up on top of it and pick up the patch.

Patch #5
There's a large building on the northwest side of Camp Omega. This is the Admin Building. Head over to the rightmost entryway (red-orange door), it's right by the huge gate that opens up to let in vehicles. Don't go through the red-orange door yet, but when you face the door, turn right and move behind the crates and cardboard boxes. By the blue mechanical device there's a drainage channel with the grate popped off. Hop in and the patch is right there, behind the bars.

Patch #6
From the previous patch, make your way over to the rightmost entrance of the Admin Building again. Go past the red-orange door. Head to the first white box-like structure that's roped off with chains and the little yellow posts. Jump on top of the container, leap to the roof on your left, and the patch is sitting on that little ventilation structure.

Patch #7
Outside the Admin Building is a helipad, and there's a windsock in the middle of the helipad. A few steps south-southeast of the windsock is the patch, sitting in a puddle of water.

Patch #8
Move southwest from the last patch, head past the chain linked fence, and you'll see three power boxes close together in another fenced enclosure near a set of warehouses. Pick open the gate, climb on top of the leftmost box, and the patch is there.

Patch #9
Roll on the ground for this one, you can do it anywhere. Hold to go prone. Then hold and push the right or left. Click down on the , and hold it down while pushing it right or left. You'll get a cutscene and the patch will dislodge from behind the pouch on Big Boss's ass.

Here’s a video guide courtesy of Maka: