You'll need a passport for sure.

If you bring a rifle (which you aren't), they will ask you to come inside the building and fill out declaration forms, that's when they will run a background check and no doubt uncover the DUI. Best thing to do is be honest with them. If the DUI was more than 10 years old, they'll probably just let you in, or pay $200 for a "pass".

If you're just entering their country to fish or bowhunt, in all likelihood they'll wave you through. It often depends on the particular crossing guard & their mood that day.

Good luck!