Big Foot is the first Boss of Hero Story, and is played with Sonic. The best possible time the player can achieve under run condition is 21.39.
The quickest strat involves moving forward to the front-left box as soon as you gain control, and repeatedly jumping off the box to deliver hits to Big Foot's cockpit. For hits 2/3/4, it is recommended that you perform a somersault as you land to accelerate more quickly.
An easier alternate strategy would be to jump on the box immediately to the left of sonic and use the boxes in the back to get airborne hits on the boss. This Strategy is about 3 seconds slower than the one mentioned above, but is drastically better than waiting for Big Foot to land.