You need to string the whole scene into one combo to get 5 stars. Easiest way to keep a combo alive is by driving close to an object or by drifting. Or if you are on a bike, you can do a wheelie by pulling the left trigger down.
I don't take credit for the video, but it can be really helpful when going for the achievement:
Timestamps for the video:
Scene 1 - Mountain Climb - 0:29
Scene 2 - Base Brawl - 2:20
Scene 3 - On Ice - 5:01
Scene 4 - The Hunt - 7:14
Scene 5 - Outage - 8:52
Scene 6 - Hover Crash - 11:10