Here is the full list of all 16 Spheroids trophies - there are 13 bronze and 3 silver.
Use the dynamite power-up 25 times
Use the stop-time power-up 25 times
Chapter 8 (Easter Island) Finished
Do a purchase in the store
Collect 1000 coins
Destroy 2500 spheroids
Chapter 7 (Greece) Finished
Collect 500 coins
Chapter 6 (India) Finished
Chapter 5 (Kenia) Finished
Chapter 4 (Russia) Finished
Chapter 3 (Egypt) Finished
Destroy 500 spheroids
Chapter 2 (Brazil) Finished
Chapter 1 (Japan) Finished
Destroy 100 spheroids