I did, multiple times (and thus on all difficulties). Use the best weapon along with the surface to ground missiles and all auto-equip weapons, get full shields (if necessary, deplete an old one at the end of a mission if it's recieved too much damage), and make sure you don't have more switchable weapons (timing is essential in that, imho). Keep four bombs ready, with the last one being pickup or money.
Oh, and always start with the Bravo sector. The other sectors are very hard without any equipment. The Bravo sector can be finished with machine guns only (I did, though not on elite yet [/brag] :P).
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