Here is the full list of all 21 Hentai Crush: Love Rhythm achievements.
Give any girl 50 Gift
Give any girl 30 Gift
Clear 16 Songs with SS Rank
Give 4 Girls 1 Credit Card each
Give any girl 10 Gift
Earn 10,000 gold
Complete Sophia & Mia's four stories
Complete all four characters' story
Earn 5000 gold
Complete Kim Hyo-rin's four stories
Clear 12 Songs with SS Rank
Complete Nara's four stories
Earn 3000 gold
Clear 8 Songs with SS Rank
Complete Shin Yeong Joo's four stories
Give any girl 1 Gift
Earn 1000 gold
Clear 4 Songs with SS Rank
Earn gold for the first time
Clear 1 Song with SS Rank
Complete first event