Successfully complete one of the following tasks to get a trophy:

Substory 10 (Bronze): Clear 10 Substories.
Substory 30 (Bronze): Clear 30 Substories.
Substory 50 (Bronze): Clear 50 Substories.
Substory 80 (Bronze): Clear 80 Substories.
Tough Guy Hunter (Bronze): Catch all Hitmen.
Big Spender (Bronze): Spend 300,000 yen in one visit to a Cabaret Club.
Good Coordinating (Bronze): Get a Cabaret Club Girl's fashion, etc. set up well in the "Groom A Cabaret Club Girl" side game.
Key Wanderer (Bronze): Open all coin lockers, both in Kamuro and Ryuukyuu.
Gourmet Master (Bronze): Order the most expensive dish at all restaurants.
Heat Action Master (Bronze): Finish a battle with a Heat Action 50 times.
Legendary Champion (Bronze): Win all tournaments at the Arena.
Trial Special (Bronze): Make one weapon at Ueyama's.
Started A Blog (Bronze): Have one Revelation.
The Path to Training (Bronze): Meet all masters/instructors.
Salon Craze (Bronze): Play two beauty-salon modes.
Hat Trick (Bronze): Get a Hat Trick at Darts.
Break Ace (Bronze): Get a Brake Ace at 9-ball billiards.
Karaoke King (Bronze): Sing all karaoke songs.
Boiled Turkey (Bronze): Get a Turkey in Bowling.
Exceptional Gambler (Bronze): Get 10,000 cumulative points at Chinchirorin, Koikoi, and Oichokabu.
Great Gambler (Bronze): Get 10,000 cumulative points at Roulette, Poker, and Blackjack.
Pro Gamer (Bronze): Get the trophies at the three games in the arcade. For the UFO Catcher, get 10 dolls. For Anser x Anser, win 10 rounds. For the shooting game, get the High Score.
Immovable Shogi Player (Bronze): Win shogi without moving the "King" piece even once.
Exposed Dragon (Bronze): Use a Naked Pair Wait (Hadakatanki) in Mahjong.
Nice Hitter (Bronze): Pass the Hard Course at Yoshida Batting Center.
Powerful Driver (Bronze): Hit a 350-yard drive in Competition Mode in Golf.
Tuna Lord (Bronze): Catch a tuna when Fishing.
Ultimate Challenger (Bronze): Play all unlockable Ultimate Fighting modes.
Marathon Runner (Bronze): Run 42,195km.
Walking Bank (Silver): Have over 10,000,000 Yen on your person.
All Substories (Gold): Complete all Substories (missions).
Mini-Game Master (Gold): Complete all Mini-Games.
Proof of Being the Strongest (Gold): Clear the game on the unlockable EX Hard difficulty.
Platinum Trophy (Platinum): Get all the game's Trophies.

Additionally, there are sixteen secret trophies:

Boss 01 (Majima) (Bronze): Defeat Majima in Story Mode's Chapter 1.
Boss 02 (Rikiya) (Bronze): Defeat Rikiya in Story Mode's Chapter 2.
Boss 03 (Tamashiro) (Bronze): Defeat Tamashiro in Story Mode's Chapter 3.
Boss 04 (Hasebe) (Bronze): Defeat Hasebe in Story Mode's Chapter 4.
Boss 05 (Mysterious Foreigner) (Bronze): Defeat the Man in the Black Suit in Story Mode's Chapter 5.
Boss 06 (Kanda) (Bronze): Defeat Kanda in Story Mode's Chapter 6.
Boss 07 (Majima II) (Bronze): Defeat Majima in Story Mode's Chapter 7.
Boss 08 (Lau Kar Lung) (Bronze): Defeat Lau Kar Lung in Story Mode's Chapter 8.
Boss 09 (Kazama) (Bronze): Defeat Kazama in Story Mode's Chapter 10.
Thank You From the Staff (Bronze): Clear Story Mode.
Runaway Train (Bronze): Knock down 100 people.
People Watcher (Bronze): Start 10 battles by staring at people in first-person mode.
Destroyer (Bronze): Break 100 weapons in battle.
Volunteer (Bronze): Pick up 5 pieces of trash at the beach in front of the Morninglory.
Boss 10 (Defeat Mine) (Silver): Defeat Mine in Story Mode's Chapter 12.
Eco-Master (Silver): Pick up 30 pieces of trash from the beach in front of the Morninglory Orphanage.