OK now that PD has increased the target times (thank god, I'd never have done it otherwise) all you're gonna need in theory is two half-decent clean laps.
It follows that the best way to complete this challenge is simply to get used to the car. It's a bleedin' horrible thing to drive because it's so fast and so sensitive. I recommend using manual gears (if you're used to manual) to at least try and gain some control over your speed, and if you're using a DS3 controller then you'll have to learn to stop turning before you actually want to. Strange and unnatural but for some reason your guy takes ages to turn the wheel where you need it in this thing. This is especially important for multiple turns in quick succession, i.e. the first section of Suzuka.
OK, the tracks.
Nurburgring: By far the hardest. The car needs a line all of its own for this track and the only way to succeed here is just to learn that line by yourself. Once you've done this, you'll probably find you can race faster here in general. Which is a plus.
Monza: Should be easy. This is a fast track and you have a fast car, so there shouldn't be much of a challenge at all here. Remember, you can cut the chicanes!
Suzuka: Many people say this is the hardest, but if you're familiar with the track this is still a pain but not as bad as the Nurburgring. On here you can take the same line as other cars which really helps. I'd run the Suzuka 1000km a couple of weeks beforehand in a JGTC NSX and after 172 laps here it's hard not to have the line completely down
If you're struggling here, I recommend doing the endurance race (will take about 7-8 hours, mind).
As has been said before, yeah, use the search function buddy. There's a gazillion threads on this, but I've got to make my contribution somewhere
