Here is the full list of all 22 Timelie achievements. It takes around 8-10 hours to unlock all of the achievements on Windows.
Collect the 3rd Memento.
Complete "Splinter Cat" relic challenge.
Complete "3-2-1-GO-1-6-7-8" relic challenge.
Collect the 2nd Memento.
Complete "This Is Cat. Can You Hear Me?" relic challenge.
Complete "Well Planned!" relic challenge.
Collect the 1st Memento.
Complete "If It Is Broken, Don't Fix" relic challenge.
Complete "A Quiet Place" relic challenge.
Complete "It'd Be Too Damned Easy" relic challenge.
Complete "Time Waits For No One" relic challenge.
Complete "Retcon" relic challenge.
Complete "The Most of Us" relic challenge.
Complete "I Come in Peace" relic challenge.
Complete "Urnique" relic challenge.
Complete "Omen" relic challenge.
Collect the 4th Memento.
Complete the story of Timelie.
Watch the secret ending.
Obtained all Timelie achievements.
Complete "I'd Like To Have That In Writing" relic challenge.
Complete "Operation Skuld" relic challenge.