Here is the full list of all 14 Ring Run Circus trophies - there are 11 bronze, 2 silver and 1 gold.
Swap characters 50 times
Complete "A Bearded Ball" without getting burned
Get on stage.
Avoid The Magician in "The Flight On Fire"
Ride one turn on the carousel
Three on the floor at once in "An Encirclement"
Complete "The Jump" with no stars
The fewest ring movements to solve "A Triple Puzzle"
Complete "A Lucky Bounce" without bouncing
The fewest character-swaps to solve "The Swap"
Hit someone with the ball
Get 50 speed boosts in a row
Hit two with a single punch in "The Lions"
Get 10 speed boosts in a row