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