There are 45 Trophies that can be earned in this title.

Bronze

Substory Dabbler
Complete 10 substories.

Substory Fan
Complete 30 substories.

Substory Enthusiast
Complete 50 substories.

Substory Addict
Complete 80 substories.

Bounty Hunter
Apprehend all hitmen.

Gourmet Aficionado
Order the most expensive item(s) in all restaurants.

HEAT Action Pro
Finish 50 battles with HEAT actions.

Tinkerer
Make a mod weapon.

Blogging Debut
Have your first Revelation.

Path of the Warrior
Encounter all the masters.

Hat Trick
Get a hat trick in darts.

Break Ace
Get a break ace in Nine-Ball pool.

Karaoke King
Sing all songs at karaoke.

Fowl Play
Get a turkey while bowling.

Tag Hoarder
Earn a combined total of 10,000 points in cee-lo, cho-han, koi-koi and oicho-kabu.

Chip Hoarder
Earn a combined total of 10,000 points in poker, roulette and blackjack.

Pro Gamer
Complete trophy conditions for the games in the arcade. Get 10 stuffed animals in UFO Catcher, and get a high score in the shooting game.
 
Skilled Hitter
Hit 2 panels with one ball in the Hard game at the batting cage.  
 
Power Driver
Hit a 350 yard drive in Competition Mode in golf.

Big Tuna
Catch a tuna.

Ultimate Challenger
Play all rounds in Ultimate Skill mode after beating the game.

Marathon Runner
Run 42,195km.

Silver

Key Collector
Open all the lockers in the top row in both Kamurocho and Downtown Ryuku.

Legendary Champion
Claim victory in all Coliseum tournaments.

Walking Bank
Accumulate 10,000,000 yen.

Gold

Substory Completionist
Complete all substories.

Minigame Master
Complete all minigames.

Testament to Strength
Beat the game on Extra Hard.

17 Secret

http://www.ps3trophies.org/game/yakuza-3/trophies/