To make a mod for any gamemaker studio game, you will need undertalemodtool. These files will help with the framework around the achievements (mainly communicating with the Retroachievements website).

Unfortunately, it's not effortless to implement this, so here's a guide. If it's unclear, or you need help with standalone modding, feel free to ask me for advice.

First, you should go to the room list and locate one of the rooms at the start (such as a splash screen, for example.)

There will be in one of the objects in it's code a room_goto_next() or a room_goto(roomnamehere). You should create a room called "RA_connect".

Then, replace the room_goto with room_goto(RA_connect).

Add a script called RA_achievement_trigger and copy and paste the code given.

Create the objects RA_achievement_hud (set this one as persistent) and RA_MENU. Put RA_Achievement_Hud and RA_MENU in the RA_connect room. (Drag them from the object list on the left into the room's image on the right. Some games may not let you do this and you'll have to create the object using instance_create_layer).

For each object, add the code in the folders to the matching category. (HTTP ASYNC is in the "other" section. There is a dropdown menu there.)

Fill in the information in RA_MENU_CREATE. You will also have to edit the code in RA_Achievement_Hud_ALARM1 to make a rich presence.

Congrats! You're done! Now just the "easy" part of coding all the achievements. To make the user unlock an achievement, use the achievement trigger example.