As Kingdom Hearts HD 1.5 ReMix is actually a collection of three separate games, the trophies have been broken down accordingly by PS3 Trophies.
Kingdom Hearts Final Mix HD
Ace Pilot - Clear Gummi Ship mission 3.
Alice in Wonderland - Seal the Keyhole of Wonderland.
Blade Master - Obtain all Keychains.
Complete Record - Complete all entries on Jiminy's Memo.
Customizer - Create your own Gummi Ship.
Friendship - Find all trinities.
Game Clear - Beginner - Clear the game on Final Mix: Beginner mode.
Go the Distance - Seal the Keyhole in Olympus Coliseum.
Gummi Ship Collector - Obtain all Gummi Ship blueprints.
Guard Master - Obtain all shields.
Magic Master - Obtain all staffs.
King of Synthesis - Create all items in the Synthesis Shop.
Mini-game Maniac - Complete the "Mini-games" section of Jiminy's Memo.
Part of Your World - Seal the Keyhole in Atlantica.
Professor - Complete the "Character Encyclopedia" section of Jiminy's Memo.
Searcher - Find all of Ansem's Reports.
Storyteller - Complete the "Story so far" section of Jiminy's Memo.
Synthesis Beginner - Create 3 item in the Synthesis Shop.
Synthesis Expert - Create 30 item in the Synthesis Shop.
Synthesis Newcomer - Create 1 item in the Synthesis Shop.
Synthesis Senior - Create 15 item in the Synthesis Shop.
Test Pilot - Clear Gummi Ship mission 1.
The Adventure Begins - Seal the Keyhole of Traverse Town.
This is Halloween - Seal the Keyhole in Halloween Town.
Top Ace - Clear all Gummi Ship courses.
Top Breeder - Find all puppies.
Top Pilot - Clear Gummi Ship mission 2.
Unchanging Armor - Clear the game without changing your equipment.
Undefeated - Clear the game without using the "Continue" option.
Will Be in My Heart - Seal the Keyhole in Deep Jungle.
Winnie the Pooh - Seal the Keyhole in 100 Acre Wood.
Wish Upon a Star - Escape from Monstro.
Whole New World - Seal the Keyhole in Agrabah.
You Can Fly - Seal the Keyhole in Neverland.
Secret Trophies
Cold Giant - Defeat Ice Titan in the Gold Match.
Coliseum Hero - Clear the Hercules Cup.
Coliseum Master - Clear the Hades Cup.
End of the World - Seal the Keyhole in Hollow Bastion.
Flying Ace - Defeat 2500 enemy ships.
Game Clear - Proud - Clear the game on Final Mix: Proud mode.
Game Clear - Final Mix - Clear the game on Final Mix mode.
Heartless Hunter - Defeat 2000 heartless.
Junior Heroes - Clear the Phil Cup.
KINGDOM HEARTS Complete Master - Obtain all trophies.
Millionaire - Hold over 10 thousand munnies.
Newbie Heroes - Clear the Pegasus Cup.
Oathkeeper - Receive the Oathkeeper Keychain.
One-Winged Angel - Defeat Sephiroth in the Platinum Match.
Single Attack Champion - Clear a cup in the coliseum with Sora alone.
Speedster - Reach The End of the World in less than 15 hours.
Stopped the level counter - Reach level 100.
The Dancing Sword in the Sand - Defeat Kurt Zisa in Agrabah.
The Non-Existant One - Defeat the Mysterious Man in Hollow Bastion.
The Shadow That Lurks in the Clock Tower - Defeat Phantom in the Clock Tower.
Time Attack Champion - Clear the time attack of a cup in the coliseum.
Treasure Hunter - Open 100 treasure boxes.
Kingdom Hearts 358/2 Days HD
Days of Connection - View Chapters 1 through 37.
Days of Reflection - View Chapters 38 through 74.
Where the Heart Lies - View Chapters 75 through 109.
Secret Trophies
358/2 Days Complete - Obtain all trophies
All Diaries Read - Read all of Roxas' diaries.
All Reports Read - Read all of the Secret Reports.
Kingdom Hearts Re: Chain of Memories HD Trophies
A Card Crafted From Your Memory - Cleared Floor 1 of Castle Oblivion
Ace Pilot - Cleared Balloon Glider minigame with a score of over 500 points
Bee Buster - Busted 70 bees in under 1min 40sec in the Bumble-Rumble minigame
Card Breaker - Broken 1,500 enemy cards
Card Master: Riku - Completed the Card Index section of D Report
Card Master: Sora - Completed the Card Index section of Jiminy's Journal
Character Professor: Riku - Completed the Character section of D Report
Character Professor: Sora - Completed the Character section of Jiminy's Journal
Duel Master - Won 100 duels
Game Clear: Standard with Riku - Cleared Standard Mode with Riku and watched the ending
Game Clear: Standard with Sora - Cleared Standard Mode with Sora and watched the ending
Game Clear: Beginner with Riku - Cleared Beginner Mode with Riku and watched the ending
Game Clear: Beginner with Sora - Cleared Beginner Mode with Sora and watched the ending
Grappling with Darkness - Cleared Basement 12 of Castle Oblivion
High Jumper - Cleared Tigger's Jump-a-Thon minigame with a score of over 120 points
Interceptor - Encountered enemies 150 times
Maximum Attacker - Riku reached maximum Attack Points
Minigame Maniac: Sora - Completed the Minigame section of Jiminy's Journal
New Card Deck Creator - Assembled first Card Deck
No Escape - Cleared the game without escaping from a single battle
Point Millionare - Currently have over 10,000 Moogle Points
Premium Card Maker - Turned 20 cards into Premium Cards
Regular Customer - Used 20,000 Moogle Points at the Moogle Shop
Room Creator - Created rooms 300 times
Skydiver - Cleared Whirlwind Plunge minigame with a score of over 2,000 points
Sleight Master - Sora learned all sleights
Spun Memories - Cleared Floor 5 of Castle Oblivion
Storyteller: Riku - Completed the Story section of D Report
Storyteller: Sora - Completed the Story section of Jiminy's Journal
The Darkness Within Blocking the Way - Cleared Basement 8 of Castle Oblivion
The Heart Overcoming the Darkness - Cleared Basement 1 of Castle Oblivion
True Memories - Cleared Floor 13 of Castle Oblivion
Undefeated - Cleared game without using continue
Veggie Master - Cleared Veggie Panic minigame with a score of over 150 points
Secret Trophies
Ace Striker - Hit an enemy with a lifted object
Advanced Card Deck Creator - Assembled 500 Card Decks
Battle Card Collector - Owns over 300 different kinds of Battle Card
CHAIN OF MEMORIES Complete Master - Obtained all trophies.
Complete Record - Completed all of Jiminy's Journal!
Complete Report - Completed all of D Report!
Game Clear: Proud with Riku - Cleared Proud Mode with Riku and watched the ending
Game Clear: Proud with Sora - Cleared Proud Mode with Sora and watched the ending
Level Count Limit: Riku - Riku has reached the highest level
Level Count Limit: Sora - Sora has reached the highest level
Memories Linking in Slumber - Cleared Sora's Story
Road to Dawn - Cleared Riku's Story
Tightrope - Healed with less than 5% HP
Treasure Hunter - Opened secret room treasure chests 10 times