Yell... achievements are just a thing that pops up on a trigger. you can build your own achievement system on your game.
You can have a single sprite with all the achievements as frames, with animation speed=0. place in on your UI set to invisible by default. and when you want it to show, depending on the trigger, you chose a frame and set it visible. then back to invisible again.
You could even store what achievements a player's got with an array and webstorage