50 cal bolt action sniper rifle with night vision scope. They are too smart to be caught off guard with any normal short to medium range setup. You need something good for 500 plus yards.
In the 200 plus years the United States has been in existence, not a single Bigfoot has ever been killed and brought in by any hunter. That alone should tell you something. Those that may have shot one, didn't live to return and tell about it so they have to be exceptionally difficult to kill.
You need something with reach, something with stopping power and something that is extremely accurate. You might not get a second shot. I'd probably want two or three guys with 12 gauge shotguns filled with 00 Buckshot as backups.