Be open, honest, and transparent with your intern mentor. Be comfortable being vulnerable, and aggressively use their time to solve issues and unblock yourself.
Set clear expectations with your mentor on what needs to be delivered in order to meet the return offer bar.
Keep your eye on the code. Intern is the stage in a SWE career where coding is the most important. A lot of interns understand that volume is important, and a lot forget that quality is important as well. Push to write beautiful code that's a joy to go over in code review for your teammates.