The Brawlin' Squirrels Achievement can be obtained on the following tracks in order by difficulty and checkpoints:
Fish and Ships (Easy) - Stop at the 6th checkpoint and wait there until the Squirrel comes up from the bushes in the background.
Seismic Activity (Medium) - Just before the 2nd checkpoint, stop and roll backwards into the opening of the building behind you.
Trials of Ice and Fire (Medium) - At the 3rd checkpoint, stop and roll backwards.
Adelopodia 9 (Medium) - Begin at the 6th checkpoint where the plant is in the water and when you reach the roof, bail out into the opening on top of the roof.
Frontside Ollie (Hard) - Begin at the 7th checkpoint on top of the circle structure. Drive forward and touch the arrow with your wheel to light up white, then reverse until you jump the gap (may need to fall into the small space and do a backflip), then touch the 3rd arrow with your back tire. After that progress forward until you reach the top of the circle structure again.