Sonic & All-Stars Racing Transformed

This achievement can be earned in split-screen.
Choose Custom Game -> Local -> Capture The Chao
Once you're in with a 2nd controller sitting idle just hit the item boxes and shoot whatever you get backwards (hold X to look backwards for easier aiming) at the 2nd player. If you get something like a Hot Rod just use it quickly and pick up another item.

This achievement can be tough to get, but the best way I found is to obviously fire as much ice fireworks and blow-fishes back at people as possible, but if you want to seriously increase your chances you want to hover in the area of 4th or 3rd-ish and wait to get a swarm, fire this backwards with back on the left stick and A, you are fairly likely to hit most if not all the racers behind you.

Since this achievement doesn't require you to win the race you can stay in this position for all 3 laps and hope for multiple swarms but you shouldn't have too much trouble getting it with just one swarm and some well aimed Ice and fireworks. To increase your chances of getting a swarm you could hang back further then overtake as many as possible and fire it back but this takes more time and you have less chances to fire anything else back.

You're best off choosing levels with no flying and preferably little or no water sections as your swarms are likely to miss in those sections. A level that is good for this is the Death Egg Zone in the Classic Cup, it's all car based and has lots of long narrow pathways which makes dodging your weapons and swarms harder for the AI.

Another way of getting this is to use Gum. (Unlocked in World Tour)
Getting her All-Star and getting up front and dropping her All-Star move behind you will gain you many backward hits. ( Credit: Salaryman Clev)

Any negative voters, please state why so I can try to rectify it.