Here is the full list of all 42 Conga Master trophies - there are 30 bronze, 8 silver, 3 gold and 1 platinum.
Perform a x2 combo
Unlock all trophies
Clear the Secret Flamingo Club
Clear Popolon Theatre
Clear Rolling Disco
Clear Magic Under The Ocean
Clear Lucky Strike Disco Bowling
Clear UFO Party
Clear Conga Heaven
Unlock all characters
Unlock The Dan
Perform a x5 combo
Perform a x8 combo
Get a cat in your conga
Enter a VIP area for the first time
Save six people from the UFO
Get a power-up for the first time
Unlock Elvira
Unlock Samuel
Unlock Martin
Unlock Freddy
Unlock Riot
Unlock Hoagie
Unlock Taylor
Unlock Bethy
Unlock Chuck
Unlock Toxin
Unlock Stephen
Unlock Walter
Unlock Isabel
Unlock Aurora
Unlock Yuzuru
Unlock Leigh
Unlock Dr.Mitt
Unlock Foxy
Unlock Denise
Unlock Jimmy
Unlock Marspeople
Unlock Karby
Unlock Purin
Unlock Otakon
Form a conga of 101 dancers