Here is the full list of all 48 A Forgetful Loop achievements.
Start the machine
Complete the first group of levels
Complete the second group of levels
Complete the third group of levels
Complete the fourth group of levels
Complete the fifth group of levels
Complete the sixth group of levels
Complete the last group of levels
Fix the machine for the last time
Fix every level
Read every story (Intros, Interludes, Outros & "The Story Before")
Fix 256 nodes
Experience 365 loops
Experience 999 loops
Skip 5 minutes worth of time
Fix a node with 4 scientists
Fix a node with 4 engineers
Fix a Time node for the first time
Fix a Goal node at the very last second
Fix a Goal node with just Students
Fix a level with 30 seconds or more on the clock
Skip 40 seconds in one loop
Assign at least 5 characters to a Fuse with 1 slot in one loop
Assign a character to a Fuse node just before it breaks
Assign a Student to a Spinner at the start of a loop, and leave them there until it resets
Spin 4 Spinners at the same time for half a loop
Fix a level with a Spinner without assigning Jennefer to any Spinners
Fix a level with a specialised Hazard node without matching the departments
Fix a level with a Hazard node by only fixing Hazards with Leads
Have a character sick from Hazard nodes for five loops in a row
Have every character from a department sick from Hazard nodes at the same time
Switch a Switch with 2 connections 5 times in one loop
Switch a Switch 5 times in one loop
Fix 2 Briefcases in one loop
Fix a Briefcase in the last 5 seconds
Fix a node with Isabel & Yolanda together
Fix a node with Jennefer & Isabel together
Have every character assigned to nodes at the same time in a loop
Assign a character to 6 different nodes in one loop, and not fix any of them
Fix a level without assigning any Students
Fix a level without assigning either Lead
Fix a level without reassigning a character while they're fixing a node
Go an entire loop without assigning anyone
Play through a group from Intro to Outro in one sitting
Grab a character as they fly back to the department sheet
Assign every role in a department to a node once in a loop
Complete the Gamejam-inspired levels
Complete every other Achievement