Here is the full list of all 28 The Lust City achievements.
Have fun with Zuli in temple
Look for Zuli's temple
Look for Arya's temple
Choose dominance
Choose submission
Choose bit of both
Start a new game!
Check Elizabeth and give her necklace
Have fun with Sofia in Bathouse
Have conversation with Xaya in front of the gates
Fun times in Chambers
Have threesome with Zuli and Lapis
Give map to Arya
Give map to Sofia
Ask Spirit of Lust about Fernando
Ask Spirit of Lust about Jyra
Have threesome with Alyssa and Elizabeth
Find crown with Arya
Ask Deshira about General and Jyra
Ask Deshira about artifacts
Talk solo to Xyla
Have threesome with Xaya and Xana at banquet
Have sex with Arya at banquet
Have sex with Xyla at banquet
Have threesome with Zuli and Lapis at banquet
Choose your favorite from the group at banquet
Have sex with Deshira
Complete the game!