Move on into the storm and carefully approach the base. There's a special achievement called “Ghost” for getting through the base stealthily, so I'll give you one course that should work. Get up next to the car and get on the ground. Carefully look out around the tire, and Soap should shoot the guard across from you. Rise up to a crouch and move past the guard on the other side of the car. Soap should take him out too. Get into the little storage hut. This guard is sleeping, so we can just ignore him.

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There's a car full of guards coming around, so move over to the red crate. Move through it and then stick to the right side of the base. Stick close to the ridge by the road. Stay crouched and in the gap. Don't climb any slopes. There's a guard on the road at roughly the 80 meter mark. If you stay low, then you should be fine.
Don't continue past the last building to the road. Drop to your stomach and crawl in between the last 2 buildings on the left. Move toward the road, but stop. Soap should pick off the one wandering guard here. Then just wait here for a moment. Hang back until the car full of guards drives past again. Look at the heartbeat monitor. If all went well, there's a beautiful gap you can go through diagonally.
Get up and crouch walk across the road. Go to the left side of the building, not the right. There's a whole guard group on the right side and we really want to avoid them. Cut to the left and get onto the runway. The group should walk out to search the runway, but that shouldn't be a problem for us. Just go down the runaway and slap the C4 on the fueling station. You should get some special recognition from Soap and the achievement right away.