I tried to do this in a Solo race but after changing the race length to 25% and wasting 45 mins of my life it never popped. It may be because I wrote the car off beyond repair (tore a wheel off) and used a flashback that it didn't pop.
So I ended up doing this in Career mode after all that.
I changed the race distance to 25% for just this 1 race. You can also adjust the difficulty of the AI if you are worried they might be better than you round the circuit.
Put in a decent qualifying session and get on Pole position. Make the first corner first and build a lead. It's hard to overtake but not impossible. My advice is to out break them on the inside of a corner.
Remember you will need to make a pit stop if its not raining, so try to build a big enough lead so you can come back out of the pits in the lead.
Once you win the race the achievement will pop/ping.