As mentioned in the guide above, this acheivement is MISSABLE.
I have gotten this with several acct's (in order to boost King Of The Hill with 2 real people) and by far the easiest way to do it is.
During the first 2 "hot laps" you have to do
1. switch the camera to chase cam
2. only beat the easy time on purpose
3. only beating the easy time lets you race against "easy" opposition in the next race and with chase cam you should nail them easily enough.
Then bingo the achievement is yours.
You still end up with the achievement and $20,000 to spend on cars whether you beat the easy, medium or hard hot lap time, but by only doing the easy time you get to race easy cars in the important MISSABLE achievement race that follows.
If you decide to beat the hard time as I did with this my main acct, then expect a few retries to come 1st in the following race
Remember you can restart the race if you have a nightmare and make sure you chose the driving options that suit your style after finishing the hot lap and before starting the race..