This solution is really only for legendary, but will be effective on any difficulty.
The only Spartan Ops mission that gave me any trouble on solo legendary was 7-1 on Apex. The difference between rock-solid success and overwhelming failure for me was the jetpack. As you make your way down the hill you must neutralize plasma barrier power supplys. When you come to the barrier with some Promethean knights, other enemies and a covenant sniper hover tower behind it (where the mantis is dropped off) do not bring down the barrier. Instead, run back up the hill a little ways, turn around and proceed to jetpack up onto the rocks to your left. From here you can find your ideal sniping position without ever worrying about taking any damage and kill every single enemy by shooting over the barrier! I personally prefer the DMR, and when you run out of ammo you can plasma grenade yourself and respawn with more bullets! If you don't have any grenades then you can run further back up the hill and jump off the cliff. There are no time constraints on this part of the mission so take your time, and kill everything! After all are dead, drop the barrier and wait for the mantis. When you get in the mantis it will trigger the friendly phantom sequence to start and enemies will begin to spawn. Watch for fuel rod grunts as soon as you get in the mantis! Fuel rods on legendary are mantis kryptonite! Head down the hill and murder everything on the way. I actually stayed in the large clearing by the phantom and fired nonstop back and forth between the upper and lower paths. Watch out for fuel rods! They will come from both paths at the same time! Early mantis destruction will most likely result in failure. My mantis was destroyed with 14 enemies left to kill and I still managed to complete the mission with a very comfortable 70% phantom health. There may be a better place to park the mantis, but this method worked very well for me. I did not find success until I killed all of the mantis area enemies before dropping the barrier.