Player characters may be minnows compared to the megacorporations, but you also have to remember that the megacorporations are in a state of constant hostility and paranoia with respect to each other, and they have a lot of other enemies. A determined group of shadowrunners might be able to wound one of the megas enough for the other sharks to finish it off, but it would take some doing.
If you want to GM such a campaign, maybe the megacorp could be vulnerable in a way that the shadowrunners could exploit. Maybe they are doing something that even the other megas would disapprove of, and are frantically trying to suppress a possible leak. Maybe they have made a really boneheaded marketing decision that could be the start of a downward spiral for them.
From the PC end, it depends on whether it is their idea in the first place or not. If it is their idea, then have them do a bit of legwork, then give them some places where they might find incriminating data, some shady dealings that they can possibly expose, and maybe some personalities they could exploit (so the head of R&D is butting heads with the head of security, hmm). In addition to this, there can be enemies of the corporation that could be convinced to be allies, some of them less than savory if you want to introduce some moral ambiguity into the mix. For it to have any chance at all, you will probably need to run a less realistic, more cinematic game - and not just gun battles, but half-assed plans working more often than they should.
If the PCs are not starting out with toppling a mega as one of their goals, they could be dragged into the initial conflict by a contact being threatened, or a job that is really a setup, or the classic dying person who hands off an explosive bit of data to the PCs, who become the next targets of corporate pursuit. Then just have the corporation act like the villains in many action movies or adventure books - instead of just leaving the hero alone with nothing but a few clues, they keep coming after him, and keep tipping their hand more and more in the process, until the hero finally beats them.