Here is the full list of all 21 Khoros achievements.
Finish your first performance
Gather 40 laurels
Gather 80 laurels
Gather 120 laurels
Gather 40 hourglass
Gather 80 hourglass
Gather 120 hourglass
Unlock Faz
Unlock Zeno
Unlock Nain and Safo
Unlock Brönte
Unlock Lykaios
Unlock Jen
Unlock Naz
Unlock Tau and Beta
Unlock Mira
Unlock Eos
Unlock Pir
Unlock Erebus
Complete all levels in Tragedy mode
Complete the Comedy mode