This is rather easy.
Setup a custom championship, I chose New Zealand with the shortest track possible.
1 Event only.
Medium AI (Or Easy)
Enable Hardcore Damage
Go in a slow car (Mini Cooper/Lancia Fulvia etc)
Complete the stage as clean as possible, do not hit anything that will damage your car.
I managed to beat the medium difficulty whilst being extremely cautious.
I personally got all these in 1 go.
1) First Hardcore Damage event won
2)First Custom Championship
3) First Win in New Zealand
4) Won without damaging my car
5)Won first custom event