Bravery will get you a win, i did it on my first run through.
There's no need to drive dirty, but pushing for speed is necessary, while being careful at the same time. The most important sections for me are the areas where you floor it.
Kart space floor it sections:
-Sorta the first big curve
-last corner into the finish line and straight.
-beware kartspace seems to have the least grip, so keep your turning very smooth.
GT arena floor it sections:
-Last two corners and straight
Silver stone floor it sections:
-A lot of places, but not many curves. No real need for strong braking on this track either. Drafting is key too.
Certainly the one of the most intense races i've had.
Not sure about the slowing down on the last lap, they seem to have no mercy for me. Barely won kart space, it was some mad crazy driving. The other races i pretty much had driving the kart down pat so i just gunned it hard, beat the last race in first for the whole last lap

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(using driving force GT)