If your dismissal is "obvious" (in the sense that it is done with a view towards denying your share) i.e., your performance to date has been good and you get the boot, as you say, "right before" a scheduled vesting date, then you probably have a case.
Enough to make an inquiry with an attorney, at least.
Talk to them first... see if you can get your options or a prorated portion of them before contacting lawyers. But make sure that you notify them that you will pursue this matter through courts if you can't settle amicably.
The AMT Tax Monster: Suppose you buy your options for $10000, and if the startup is acquired or publically traded and your shares are worth $90000 at the end of the year, then the IRS will say that you earned an extra $80000 in short term capital gains ... WHETHER OR NOT YOU SOLD THE STOCK! You still have to pay tax on that change in value. That's a "feature" of the AMT tax. So you pay the IRS an extra $22000 in taxes. You're now down $32000. Finally after 30 months you sell the stock for $38000. So overall you gained $4000 plus and if you know which forms to file you can get a tax deduction for the extra tax you paid before... up to certain amount.
So don't buy your options unless you're absolutely certain the stock will be worth a lot more than what you paid for it and you can sell it quickly at any time.
It's the equivalent of getting punched in the mouth and then thanking the guy who hit you!
Also, if he really was tossed out unfairly, his buying stock ruins whatever legal case he might have.