I keep track of all the DS game i have beaten, so here is the list so far.
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GAMES WITH THE MAIN STORY HAVE BEEN COMPLETED BUT HAVEN'T UNLOCK EVERYTHING
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007 - Quantum of Solace (Completed main game, haven't upgraded all weapons)
Big Bang Mini (Completed main game, haven't complete all modes)
Bionicle Heroes (Completed All levels & unlocked all cheats, but haven't collected all secrets from each level)
Bomberman Land Touch! (Completed Normal Story Mode & unlocked all characters, didn't get 999 in "bomber house game +" & Hard mode)
Call of Duty: World at War (Completed main game, haven't completed all goals)
Cooking Mama 2 (Almost completed all meals, & let's cook mode)
Crash of the Titans (96% Completed story mode & unlocked all art & hacks, haven't collected all the gems)
Death Jr. & the Science Fair of Doom (Completed story mode, haven't unlock everything by rescuing the kids)
Dragon Ball: Origins (Completed main story, haven't gotten S rank in all episodes, haven't unlocked all 3D model statues)
Kirby: Canvas Curse (Completed story mode as kirby, didn't unlock everything, didn't beat best time & use less ink challenage)
Kirby: Squeak Squad (Story mode completed, haven't completed the other modes)
LEGO Star Wars: The Complete Saga (96.5% Completed all episodes, unlocked everything but haven't collected all gold pieces)
Ninja Gaiden: Dragon Sword (Completed story mode, haven't unlock all difficulty setting, & unlockables)
Ontamarama (Completed story mode, haven't unlocked everything)
Osu! Tatakae! Ouendan 1 (Completed all songs on all difficulty, haven't achieve S Ranks in all songs)
Resident Evil: Deadly Silence (Completed classic mode as Jill, but not as Chris, and haven't done any in Rebirth Mode)
Sonic Rush Adventure (Completed story & beaten final boss, haven't completed every mission)
Spider-man: Friend or Foe (Completed story mode, didn't unlock everything in the shop)
Super Princess Peach (Completed Story mode, haven't played post levels & haven't unlocked everything)
The Legend of Zelda: Phantom Hourglass (Defeated the last boss, completed all side quest but haven't gotten all gold ship parts)
The Simpsons Game (completed story mode, 97% haven't completed 100% for each episode)
Touch of the Dead (Completed on easy & normal, didn't unlock everything)
Transformers: Autobots (Completed story mode, haven't unlock all the cheats & Cars through wi-fi mode)
Viewtiful Joe: Double Trouble (Completed story mode, didn't unlock V-Mode by completing Adult mode)
Wario: Master of Disguise (Completed story mode, didn't play special eps & didn't get $200,000 in treasure)
Warioware: Touched! (Completed story mode, didn't beat every microgame within a certain score)
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GAMES WITH 100% COMPLETION
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Alvin & The Chipmunks (Completed on all difficulty)
Apollo Justice - Ace Attorney 4 (All Episodes Completed)
Assassin's Creed - Altair's Chronicles (Completed story mode)
Bleach: Blade of Fate (Completed story mode, everything unlocked)
Bomberman (Completed Normal Mode)
Brothers In Arms DS (Completed solo campaign on all difficulty & awarded all awards)
Call of Duty 4: Modern Warfare (Completed story mode)
Contra 4 (Completed Arcade & Challeage mode & unlocked all bonus content)
Cooking Mama (Comleted all meals, & let's cook mode)
Crash Bandicoot: Mind Over Mutant (Completed the game, & collected everything)
Dementium: The Ward (Completed the game)
DK: Jungle Climber (100% completion, haven't got AAA rank in some challenges but they are not needed)
Dragonball Z: Super Sonic Warriors 2 (Completed Maximum & Story Mode, everything unlocked)
Drawn To Life (Completed story mode & unlocked everything)
Elite Beat Agents (Completed story mode on all difficulty, unlocked all bonus songs)
Hotel Dusk: Room 215 (Completed with the extra scene at the end)
Insecticide (Completed story mode)
Iron Man (Completed story mode with all upgrades)
Jake Hunter: Detective Chronicles (All episodes completed & passwords unlocked)
Lara Croft Tomb Raider: Legend (Completed story mode & unlocked everything)
LEGO Batman - The Videogame (Completed story mode & unlocked everything)
LEGO Indiana Jones: The Original Adventures (Completed story mode & unlocked everything)
Little Red Riding Hood's Zombie BBQ (Completed all modes on all difficulty settings)
Mario & Luigi: Partners in Time (Completed story mode)
Mario VS Donkey Kong 2: March of the Minis (All gold stars, & Mini cards)
MECHassault Phantom War (Completed story mode & unlocked everything)
Nanistray 1 (Completed Adventure, Challenge & unlocked everything in the gallery)
Nanistray 2 (Completed Adventure on all difficulties, Challenge & unlocked all simulators)
Naruto Ninja Council 3 (Completed mission mode)
New Super Mario Bros. (Completed with the maximum 3 star rating)
Osu! Tatakae! Ouendan 2: Moero! Nekketsu Rhythm Damashii (Completed all songs on all difficulty with S Rank)
Phoenix Wright - Ace Attorney 1 (All Episodes Completed)
Phoenix Wright - Ace Attorney 2 - Justice For All (All Episodes Completed)
Phoenix Wright - Ace Attorney 3 - Trials and Tribulations (All Episodes Completed)
Professor Layton & the Curious Village (Completed all main puzzles & story, done all weekly puzzles)
Rayman DS (100% completed, collected everything)
Sonic Rush (Completed Sonic's & Blaze's story & beaten final boss)
Spider-Man: Web of Shadows (100% completion -Does not save after last boss fight-)
Star Wars: Lethal Alliance (99% completed -Can't get 100% due to story mode saves right before last boss battle & not after-)
Star Wars: The Force Unleashed (Completed story mode & unlocked everything)
Super Mario 64 DS (Collected all 150 stars, & unlockable REC room mini-games)
Super Monkey Ball: Touch & Roll (Completed all stages)
Teenage Zombies: Invasion of the Alien Brain Thingys! (Completed adventure mode)
The Incredible HULK (Story mode completed & unlocked everything)
The Legend of Spyro: Dawn of the Dragon (Completed story mode)
The Legend of Spyro: The Enternal Night (Completed story mode)
TMNT (Completed story mode, all levels have gold medals)
Tomb Raider: Underworld (100% completion, unlocked everything)
Touch Detective 1 (Completed all episodes & bonus episode & unlocked everything)
Touch Detective 2 1/2 (Completed all episodes & bonus episode & unlocked everything)
Trace Memory (Completed with good ending)
Transformers Animated: The Game (100% completion, unlocked everything)
Trauma Center: Under The Knife 1 (Completed story mode & extra challenges -Ranks are either A or S-)
Yoshi Island DS (Completed story mode)