Here is the full list of all 40 Persona 4: Dancing All Night (EU) trophies - there are 21 bronze, 15 silver, 3 gold and 1 platinum.
Obtained all trophies
Seen all Bond Fevers between Yu and Rise
Triggered all dances/Bond Fevers with Nanako
Seen all Bond Fevers between Yosuke and Teddie
Seen all Bond Fevers between Yukiko and Chie
Completed the Database
Obtained all accessories
Bought all costumes
Unlocked highest difficulty (ALL NIGHT)
Used a total of P$500,000 in Shopping
Bought half of all costumes
Bought all items in Shopping
Watched all events, including pre-story
Cleared all tracks in Free Dance
Performed a full combo on a track
Obtained top rank (King Crazy) on a track
Cleared a track with each character in changed costumes
Margaret joins the dance
Got through to Mikuratana-no-Kami
Triggered 30 types of Bond Fevers
Rescued Kyoka Ochimizu
Completed Chapter 4
Rescued Nozomi Nakahara
Equipped accessory and began dancing
Seen all Bond Fevers between Naoto and Kanji
50%+ Perfect clear on HARD track or higher
Beat your own high score
Danced using 2 or more items to raise difficulty
Rescued Sumomo Ujima
Paired Rise and Kanami in Free Dance
Rescued Tomoe Sayama
Rescued Tamami Uesugi
Watched replay data from Score
Cleared a track with no MISSes
A performance ended prematurely
Changed costume and began dancing
Bought a costume for the first time
Triggered a Bond Fever at least once
Completed Chapter 1
Cleared 1 track in Free Dance