This achievement is a timed achievement for beating the story. You must beat the game in under 1 hour and 15 minutes in order to get this achievement. Save this for your 2nd, and play it right after your first (or at least within reasonable time frame). If you "save it for later" you'll end up having to relearn the game again. You will want to stack this with the "Cuddles" achievement for not killing any humans. Speed through to the main objectives and grab only the grub you have time for. If you spot a challenge, it's a good option to get some extra upgrades from the grub you can earn. Challenges do not count for your time limit, nor for your kills. Once you have enough, upgrade your speed first and then the silent walking. After that, ignore all grubs and challenges. Always look for shortcuts, as some of these will save you a ton! It's a great idea to have a backup save.
Here are some examples of times that you may wish to go for:
30 Minutes: Reaching Containment for the second time.
40 Minutes: Should save the floating guy imprisoned in the dome.
55 Minutes: If you make it to the sub by this time, you're in great shape.
1 Hour to 1:10: In between here you should get to the boss and defeat him.
Tip: Remember to hold to skip cutscenes. When you die, dashboard. Every time you "retry" it seems to save your time. When you respawn at a checkpoint, the first thing it does is give you another checkpoint at that spot. So instead of selecting "continue", just dashboard. This will help in reducing your time severely depending on where you are in the game.