Second pillar with the spikes has a ladder on one side. Climb them up and jump the platforms.
After the first flower the treadmill will go below a platform. On the other side, spin to destroy the boxes and reveal a jump pad. Go to the right for the diamond.
From the checkpoint, don't follow the main path but go left to find a jump pad. Go right and jump over the spikes.
Continue the path until you see a bee on a higher platform on the left side of the path. Let the platforms switch until you get a jump pad next to the bee's platform. Jump up and watch out for the bee.
Achievement will pop up when you pick the last diamond, so you can either do this with a normal playthrough or have an extra run for it and quit after it pops.