Go in the building at the start of the mission to participate in a free-for-all boxing match. The first round has you defeating 20 wolf enemies, which shouldn't pose any problems at all. If you need any health, then break the debris being thrown into the ring. The second round has you facing the champ, as well as the same enemies as last round. Just concentrate on the big guy until its health is depleted all the way.
The second part of this mission has you racing with Sly's jail costume. This is a pretty challenging course, since if you fail, then you have to start from the beginning. It's also timed, with each checkpoint consisting of around 30 seconds or so. Things are smooth sailing until after the second checkpoint, where you'll encounter TNT barrels in close proximity to each other. After that, it shouldn't be too bad, but be careful of the dynamite being thrown, which are easy to locate due to the red circle on the ground.
The third part of this mission has you in a shooting competition using Carmelita Fox. You need to amass 100 points by shooting targets that pop up. The ones that are greenish-blue in color will cost you 1 point, the ones that are brown are worth 2, and the monkey-shaped ones are worth 5. There's one other target that swings in the far back, but it's unknown whether this gives you or costs you points. Get 100 points in the time limit to win and finish the mission.