Haven’t been through an acquihire process myself, but I am familiar with this sort of thing.
Yes, you should have an NDA and other agreements (e.g. an MoU) before you divulge serious details. Think of it like this: there are two possiblities, and you can’t know in advance which is true: 1)BigCo is acting in good faith, 2) BigCo is acting in bad faith. In the first you have nothing to worry about. But if it is the second, after they’ve figured out exactly how you’ve implemented things, what exactly stops them from having their own techs build in a few weeks/months? An NDA/MoU or any other agreement doesn’t mean you’ll definitely sue them if they screw you over (mainly because you’re not that rich), but it will give them just cause to think long and hard before doing so. If you have signed paperwork validating your stand, you can (theoretically, but also practically) raise a stink about the whole business, if they turn out to be “dishonest”.
The more potential leverage (i.e. legal documents) you have, the greater the opportunity cost for them to screw you over - much easier to simply buy you out instead of copying your tech, and risking a furore in the media, and possibly with customers.
Understand that this is just business - just cost and benefit. They obviously have much to benefit from your tech, else they wouldn’t be pursuing you. Make sure the potential cost of possibly screwing you over is high enough. If it is cheaper for me to simply copy you and profit, and know that you can’t do a damn thing about it, I’d be damn stupid not to.
That being said, don’t be a dick to an acquirer if you want to get acquired. Be upfront and ask for the paperwork. Call it a proof of good intentions. If they are genuine, they’ll appreciate your situation and arrange it quickly. If they don’t that’s your first sign of trouble.
Good luck.