After completing the 'Meet the contestants' mission, you'll have access to the bike's workshop, which can be found inside a trailer near the Yucatan Casino entrance on the Platinum Strip. You can attach items, such as a chainsaw to the bike.
Simply fetch a chainsaw, located in the maintenance room directly across the Slot Ranch Casino entrance on the Silver Strip, and bring it back to the trailer. Attach it to the bike and you have yourself a brand new Slice Bicycle.
You can make tours on the Silver/Platinum Strip until you have 1000 kills, but it's best to save this for case 6-3 when you're about to save Rebecca, since you can complete another achievement (Having a Gas) at the same time.
Make the Slice Bicycle as explained above and take it underground through the hole that's revealed in the Case 6-3 cut scene. Once there, start making circles through the underground tunnels. You'll be able to earn both achievements at the same time, thus saving precious time in your playthrough.?
You can use this picture for guide dance to obtain this achievement.