Here is an explanation from the walkthrough:
Move the geese around until the fox is cornered in the area you need.
The strategy is to herd the fox (pig) by surrounding him with the geese squares placed one square away from the fox (pig).
Move the pig area geese down and slowly surround the opponent. Leave a space on the area you want to herd the opponent in (usually the corners). The side area geese that is not in play might need to be moved to the fox area to block the opponent going-hiding back there.
When you get close to the opponent be sure that it can not jump over the goose so that the goose is taken out.
Some sacrifices might need to be done to herd it in the corner though. Be sure to have the back and sides of the goose covered.
The win makes the eye of the animals glow and the bars in the vault maze will be removed.
There is also a video of the game being played here.