Visit his shop and purchase the Hunter's Guide for $5.00.
You have to go to the marked locations and use the “baits”. You have to report back to Jimbo after defeating the targets. You can take them in any order you like though some of them can only be accessed as you progress through the story.
Rabid Junkyard Dog
East of Kenny's house. Use Moldy Sausage to lure him.
Farm Cow
Attach the cow bell near the fence to call the cow. Hit it with your weapon to complete the task.
Penis Mouse
You can find its lair deep inside the sewers. The entrance is found in the open manhole outside the news office. It is also important that you need the alien probe tool that can be acquired during the main quest “Alien Abduction”
Use the alien probe to beam yourself to the other side. Take the ladder down then shoot the valve to moderate the sewage flow. Go past it and operate the yellow valve to stop it completely. If you're still doing the sidequest “Manbearpig”, the generator there is where you'll have to place the Defilibrator.
Go around the corner and continue to the left. Pull the lever to access Mr. Hankey's home. After a scene, a new sidequest will become available. (Dropping the Kids Off)
Once you've reached the part of the sewer where you defeated one of the homeless settlements, continue to the right and pull the switch that's hiding behind a destructible wooden plank.
Go upstairs, place the bait to summon the mouse. The battle is very straightforward and no special tactics will be necessary.
Fruit Bat
You can do this while exploring the whole sewer system. After finding Mr. Hanky's kids during the quest “Dropping the Kids Off”, continue exploring the sewer until you reach a cavern with a drumming crab person. Just go past it for the meantime and continue to the far right. Once you've reached the ladder, take the lower path and place the bait there to summon the Fruit Bat. After defeating it, you can climb up the ladder to open up an alternate entrance near the cinema.
Mutant Bacteria
During the quest “Attack the School”, you'll reach the basement area. Continue until you see the door labeled “Boiler Room”. Head inside and place the rubbing alcohol on the green culture dish to trigger the battle. This should be an easy battle even if the enemy has enormous amount of HP. Use multiple status effects, preferably Froze, Burning and Bleeding damage.
Barking Spider
Once you've reached Canada as part of the main quest “Heading North” and “O Canada”, head to the northeast portion to find a spiderweb in the overworld map. Place the bait there and fight the last game target. This is just a simple battle so no special tactics necessary.
Once you talked to Jimbo again and killed all the targets, the quest will be complete.
Rewards:
Jimbo's Key – Reach the chest overhead by using the alien probe in the right side of the room.
New Friends: Jimbo, Ned