I checked solutions for this before tackling it myself and most seem to recommend holding down the airbrakes and crawling around the track in what would end up being a 15-minute lap. That is a possibility, but this isn't that difficult to do at full race speed.
By far and away the hardest section is the beginning of the entire track with that double chicane down into the tunnel, followed by the fast exit out of the tunnel. I found the best way was to slow my self slightly on the approach to lap start and aim for the middle of the first set of speed boosts (to avoid triggering them). Take the first chicane and try to keep right, again avoiding the speed boosts. On this brief bit of straight hit both airbrakes for a second or so to slow your approach into the tunnel entrance chicane, which should stop you from hitting the wall on the way in.
Once you clear the tunnel the rest is largely plain sailing as the remainder of the track is fairly wide and accommodating. The final corner could be a little tricky if you hit a few of the speed pads, but you'll get the feel for it. I managed to do this after about 10 or so laps, just getting a feel for the track using the Pir-hana Prototype and then nailing that first section.