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