Any character can ride the below rides, however, if you choose a flyable character this will speed up the process to get each of the rides.
You will need to travel to the Amusement Mile area which is available from the view map and fast travel of “Joker’s Fun House”.
1. The Curious Carousel this has a Riddler icon on top, to ride this you are required to tap the

button.
2. The Wheel of Misfortune, to ride this you are required to tap the

button.
3. The Dodgem 53 Cars, there will be 2 figures battling it out on there. You will need to smash the large box and use the electric ability to lose power, so that they leave their 2 dumper cars.
For now move onto number 4 roller coaster and complete, to activate next power source.
Once number 4 complete a new power source will have spawned to smash open door using a flash or reverse flash on treadmill and finally supplying with an electric source to ride a dodgem car.
Sorry, this Game Clip has been removed
4. The Rollin' Poison rollercoaster you need to do the following to ride:
Turn on power
Key in 3 digit code which is 3 - 1 - 2
Use D Pad on green arrows console
Now tap

to jump in a car to ride
5. Helter Skelter fly to the top or run up it and tap

to ride.
Fly up to the top and ride it down collecting all the coins on the way down.
*Please note that you may need to complete certain hub missions of story levels to complete this as I did once finished level 12, also for the bumper car section I killed the power and had to move onto the roller coaster first before I could turn power back on with a new power source and character types to activate*As soon as you jump into the 5th ride, pop achievement unlocked.
Congratulations!
Happy Hunting