Edit: Updated with secret trophies courtesy of jonny_bolton.  Please refrain from posting incomplete trophy lists. ~Watchful

Bronze: 42, Silver: 6, Gold: 2, Platinum: 1, Total: 51

Bronze

Warrior
Won 5 or more battles in Online Mode.

Gladiator
Won 25 or more battles in Online Mode.

Rookie 
Competed in 10 or more battles in Online Mode.

Veteran 
Competed in 30 or more battles in Online Mode.

Champ 
Competed in 100 or more battles in Online Mode.

Striker 
Executed a counter-attack at least 10 times in Versus Mode or Online Mode.

Sniper
Executed a counter-attack at least 30 times in Versus Mode or Online Mode.

Bull Fighter 
Inflicted critical counter-attack damage at least 10 times in Versus Mode or Online Mode.

Slow Starter 
Cleared Arcade Mode within 10 minutes.

Speed Star 
Cleared Arcade Mode within 8 minutes.

Cannonball 
Cleared Arcade Mode within 6 minutes.

Crown Jewel of Taekwondo (Hidden)
KO'ed every character in Arcade Mode using Kim.

Conqueror (Hidden)
Cleared Arcade Mode without using CONTINUE.

RANK F Bronze Trophy (Hidden)
Achieved Rank RANK F in Online Mode.

Strongest Tiger (Hidden)
KO'ed every character in Arcade Mode using Robert Garcia.

Silent Soldier (Hidden)
KO'ed every character in Arcade Mode using Leona Heidern.

Scion of the Flame (Hidden)
KO'ed every character in Arcade Mode using Kyo Kusanagi.

Psychic-Powered Idol (Hidden)
KO'ed every character in Arcade Mode using Athena Asamiya.

Out-of-control Tank (Hidden)
KO'ed every character in Arcade Mode using Raiden.

Legendary Wolf (Hidden)
KO'ed every character in Arcade Mode using Terry Bogard.

One-Man Army (Hidden)
KO'ed every character in Arcade Mode using Ralph Jones.

Tough & Cool (Hidden)
KO'ed every character in Arcade Mode using Clark Still.

Shooting Star (Hidden)
KO'ed every character in Arcade Mode using Benimaru Nikaido.

Human Weapon (Hidden)
KO'ed every character in Arcade Mode using Andy Bogard.

Shanghai's God of War (Hidden)
KO'ed every character in Arcade Mode using Shen Woo.

Unbridled Instinct (Hidden)
KO'ed every character in Arcade Mode using Iori Yagami.

Rising Storm (Hidden)
KO'ed every character in Arcade Mode using Goro Daimon.

Invincible Dragon (Hidden)
KO'ed every character in Arcade Mode using Ryo Sakazaki.

Drunken Fist Master (Hidden)
KO'ed every character in Arcade Mode using Chin Gentsai.

Young Rising Dragon (Hidden)
KO'ed every character in Arcade Mode using Sie Kensou.

Silent Assassin (Hidden)
KO'ed every character in Arcade Mode using Duo Lon.

Young Champ of Muay Thai (Hidden)
KO'ed every character in Arcade Mode using Joe Higashi.

Conductor of Brilliance (Hidden)
KO'ed every character in Arcade Mode using Elisabeth Branctorche

Cruel Beauty (Hidden)
KO'ed every character in Arcade Mode using Mature.

Sneering Blaze (Hidden)
KO'ed every character in Arcade Mode using Ash Crimson.

RANK A (Hidden)
Achieved Rank RANK A in Online Mode

RANK S (Hidden)
Achieved Rank RANK S in Online Mode.

RANK E (Hidden)
Achieved Rank RANK E in Online Mode.

RANK D (Hidden)
Achieved Rank RANK D in Online Mode.

RANK C (Hidden)
Achieved Rank RANK C in Online Mode.

RANK B (Hidden)
Achieved Rank RANK B in Online Mode

RANK SS (Hidden)
Achieved Rank RANK SS in Online Mode.

Silver

Hero
Won 50 or more battles in Online Mode.

Master
Competed in 300 or more battles in Online Mode.

Razor Edge
Executed a counter-attack at least 50 times in Versus Mode or Online Mode

Lightning
Cleared Arcade Mode within 4 minutes.

RANK SSS (Hidden)
Achieved Rank RANK SSS in Online Mode.

Perfect Fighter (Hidden)
KO'ed every character in Arcade Mode using all of the characters.

Gold

Legend
Won 100 or more battles in Online Mode.

Speed King 
Cleared Arcade Mode in under 3 minutes and 30 seconds.

Platinum

King of Fighters 
Unlock all trophies.

Source: http://www.ps3trophies.co.uk/showthread.php?t=30842