Judging by the description this appears to be really straightforward so this may seem like an unnecessarily long solution, but I had some trouble in unlocking this (Confusion may be a better term!) so thought I'd post some details on how I did it, in case anybody else is experiencing anything similar.
After trying this in both quick race and career mode, completing several races in helmet view this did not pop (I'm still not sure why or what I did wrong!). I ended up unlocking this in an Offline Multiplayer race. You don't even need a second controller and guest account, as you race individually, one after the other, as opposed to all at once.
If you're like me and just looking to get this out of the way quickly, set up an Offline MP race on either Milford Street Circuit or Tyrone Track. They're the two shortest tracks in the game. Tyrone Track is the longer of the two, but has a few less harsh corners so may be the smoother/easier ride.
Just choose 1 lap, pick whatever time of day you want and start the race. The description implies you have to ride the complete race in helmet view, so to make sure you are in helmet view right from the off, before you start the race, go to Options, then Video > Camera > Default Camera.
The achievement should unlock immediately after the first person has completed their lap, so you don't even need to complete the subsequent laps if you so wish.