Take a hit from a projectile enemy (tank, toastbot) while the puppy is moving upward. You have to time your jump right to get the boost.
Damage boosts can be either inbounds or out of bounds, depending on where you end up.
The Royal Museum donut boost is risky but does save time.
If you're playing All Puppies on PC, the Underground boat boost is the fastest route. The Lumber Mill damage boost (GIF above) is slower than the currently-used bulldozer clip in All Levels (OoB).