Extricate

In order to get the dev medal on a level, you need to beat it QUICKLY. Like, REALLY fast. The time to beat is displayed in both the level select menu and leaderboard. You'll need to do this for all 50 levels in the game—a tricky and time-consuming task! It took me over 50 hours to do it, though many others have done it faster.

First, you need to learn how the bunny hopping movement actually works. Basically, you strafe left and right while moving your mouse in the same direction you're strafing to gain speed, all while holding down spacebar in this game (in Source Engine, you'd bind jump to the scroll wheel, but in this game it's much easier on the hands). There are plenty of YouTube videos online that outline the mechanic in Source games (i.e. Garry's Mod, Half-Life 2), but it's a lot easier in Extricate than in those. Just practice a bit; A2 is good for this. You'll get the hang of it in no time.

Always look through the replays for routing. You can see these by checking the leaderboard for a level (accessible via the pause menu). The first section of levels (section A) is tough due to the levels being short and the time requirements being tight. The levels are easy to complete, but for dev medals? They're a bit of a challenge! They'll get you good at bunny hopping if you're not already accustomed to it. Section B and C are hard, but not too bad. Some levels in Section D are quite difficult, though, and Section E has a few levels that are absolute hell to get the dev medal in. However, with enough time and patience, you can do this. Just throw on your favorite music and power through them if you want to get them all.

Use these videos for more help:

A compilation of all of my replays. I tried to make the routing as easy and logical as I could for most levels.
https://www.youtube.com/watch?v=4MAA4zOmFqg

AmirGaris, who showcases recordings of the runs instead of replays (do take into consideration that he played this game before it was nerfed; routing is similar, though):
https://www.youtube.com/watch?v=KP8lj28uX4c

There are quite a few others on YouTube as well if you need them. Good luck!

(Also, take some breaks. This game can be taxing on the hands.)

This achievement isn't nearly as bad as it sounds. Just take it super slow and you should be alright. Make sure you don't die too much before Section E, because there are quite a few sections to navigate here that are more difficult when absent of bunny hopping momentum. I recommend doing the "Speedrunner III" achievement first to familiarize yourself with the speedrun mode style of play, plus to get a refresher on some of the earlier levels.

Note: the previous bug in which you needed a PB for the sub-11 death run to count for "Careful" has been fixed. You can now get this achievement on any run, regardless of if it's your personal best.