Here is the full list of all 42 Conga Master achievements.
Unlock Riot
Get a cat in your conga
Clear Rolling Disco
Clear Popolon Theatre
Perform a x5 combo
Enter a VIP area for the first time
Get a powerup for the first time
Unlock Bethy
Clear the Secret Flamingo Club
Perform a x2 combo
Clear Magic Under the Ocean
Clear Lucky Strike Disco Bowling
Clear UFO Party
Unlock Conga Heaven
Form a conga of 101 dancers
Unlock all characters
Perform a x8 combo
Save 6 people from the UFO
Unlock the Dan
Unlock Elvira
Unlock Samuel
Unlock Martin
Unlock Freddie
Unlock Hoagie
Unlock Taylor
Unlock Chuck
Unlock Toxin
Unlock Stephen
Unlock Walter
Unlock Isabel
Unlock Aurora
Unlock Yuzuru
Unlock Robin
Unlock Dr.Mitt
Unlock Foxy
Unlock Denise
Unlock Jimmy
Unlock MarsPeople
Unlock Karby
Unlock Purin
Unlock Otakon
Unlock all achievements