This is not a particularly easy job with the engine in your car, but it may be possible nonetheless. It happened to me quite similarly in November and I was able to repair mine. I suspect a previous mechanic had taken off and put the A/C compressor on without much adeptness.
In your case, if you can do it without spending $500, it could still take you alot of time. Ideally you'd have someone with experience in such repairs help you. But it is so much easier to do without the engine in your car that I'd recommend you not attempt it unless you are very skilled.
Which bolt is still intact? The one at the top or one of the two on the bottom?
The top bolt end can be easily reached from above in the engine bay if it needs removal from your engine block and retapping. If some of it protrudes from the block, but won't turn with vice grips, or some form of bolt extractor, perhaps you can have someone weld another similar sized bolt's threaded end to it to give you a good bolt head to turn. Heat is helpful in breaking corroded threads loose. [ I hired a skilled mechanic to extract one similar bolt that holds on the A/C belt's adjusting pulley bracket to the engine block a year before .... and because its broken end that fortunately protruded from the block far enough to weld onto, was very corroded and stuck in the block, he wasn't sure he'd get it out... but finally with heat from a torch, with the welded-on bolt as an extension, and much force, it did finally turn out... for a well-deserved $40.]
If you attempt to first drill out a broken bolt end, it's really important to use a sharp center punch to indent the center of the broken bolt first before drilling. You don't want your drill to end up drilling off center and damaging the threads in the engine block. If you do, the new bolt won't be as strong. Or you might need to insert a "time-sert" or "helicoil" to create new threads.
You'll have at least one of the lower bolts that is broken to also extract. Believe it or not, it's possible to do that from above too. To drill in that narrow space (you've got 6 to 8" between the bolt and the firewall, right?), you'll need a right angle drill. The best I've seen is an air-powered drill with a right angle drive because it doesn't need much room. Or you can buy a right angle adapter for a conventional electric drill at many hardware stores so that adapter and drill bit can drill into the broken bolt's centerline. To keep the adapter from spinning when mounted on my drill, I clamped a heavy hose over it to bind it to the stationary end of the drill with hoseclamps. If you want a picture, I'll post one. Now, how can you exert enough pressure on that drill bit from up on top? I used a flat pry bar between the end of the right angled adapter and the firewall to apply pressure while drilling. It worked. But only use the very best quality, high strength (?titanium?) new drill bits you can find! You don't want a dull drill bit to spin without biting into the broken bolt or worse yet, to slip off and drill off-center and partially into the engine block beside the bolt. Even worse yet, you don't want to break the hardened drill off in the hole before you've drilled sufficiently deep to retap the hole...for you might not ever get it out.
The tube that connects the a/c compressor to the radiator is rather difficult to move aside; but you might slip the insulation layer off after removing the clamp to at least get some working distance there. If you leave your A/C compressor attached (to keep from losing freon), you'll have to strap it down as far away from the working area as you can. (possible but awkward).
You'll need at least 2 of those three bolt holes intact to restrain the A/C compressor afterwards. 3 is preferable though, and that's what Toyota intended. With only two bolts, the A/C compressor isn't secure enough in relationship to the engine block and will tend to flex the remaining two bolts, possibly causing them to break in the future. There however is a fourth (unused) bolt hole in the engine block that might be used to supplement the holding power and stabilizing force of just two good bolts. Unfortunately, it doesn't line up with the unused upper driver's side mounting flange atop the A/C compressor and for that reason wasn't used by Toyota in the MR2. But with a metal bracket, some various bolts, washers, lots of patience and trial and error design and fabrication time, and some ingenuity you can adapt that engine block's fourth threaded hole to secure the A/C compressor if you only have two other good bolt holes available. (i.e. because you couldn't extract one of the other bolts) See the photos below for an idea of this improvised solution.
Again, it's better and faster to do it right and drop the engine for this repair... depending upon your success in extracting the broken bolts. With global warming looming in our future, you'll need your A/C to be reliable!