Here is the full list of all 15 Double Dragon Trilogy achievements. It takes around 4-5 hours to unlock all of the achievements on Windows.
Have more than 10 game over
Use the travelator in stage 2 (DD2)
Beat the Terminator Boss in 2nd stage (DD2)
Make 100 hurricane kicks (DD2)
Use all the weapons of the game (DD1)
Complete DD1 Story mode
Complete a lvl without taking a hit (DD1)
Start all 3 games
Start a Multiplayer game (local or online)
Make a 50 000 pts score (DD1)
Complete DD2 Story mode
Complete DD3 Story mode
Complete DD1 in Arcade and expert mode
Complete DD2 in Arcade and expert mode
Complete DD3 in Arcade and expert mode