Mega Man X Legacy Collection

NOTE: Must be done on the run where you kill the boss. You cannot return to the stage after defeating them to unlock the achievement. (Thanks to Robster80 in the comments for the info!) Also, you cannot get spotted and then die, it has to be done in one flawless run (Thanks to MegaManSurvives in the comments). It does take a bit of practice (I think it took me about an hour to get it right), but it isn't one of the hardest achievements I've obtained.

Here is a password that takes you to the next boss as Magna Centipede, to make things easier. (Thanks to Shi Kiseichu for the PM of this!)
6184
3367
3188
7583

This took me a few tries to unlock. In order to do so, you must not touch any of the spotlights seen in 2 sections of the level. You'll know you've touched one when the screen flashes and a siren goes off.

The first section I found trickiest. Using charged shots followed by regular buster shots, take out the enemies patrolling the area. Once you've done this, use the walls as cover from the spotlights. The first few are simple, but the last two in this section are tricky - what I did was use a charged Speed Burner shot and jumped to hit the edge of the high platform when the spotlight was on it's way to the right. This should give you enough time to get up and behind the wall to avoid detection. Once this spotlight heads to the left again, dash to the right and you should narrowly avoid hitting the bottom spotlight.

Now, make sure not to get crushed by those huge boxes! I made that mistake before. Just be super careful. On to the second set of spotlights!

These appear after you've defeated the wire-frame sword miniboss. In hindsight, these are much simpler than they seem, and much easier than the first section. There are two sets of spotlights. To avoid the first, when you've progressed past the previously mentioned miniboss, you'll come across a pit with a large health to the right. Simply hang right as soon as possible and hold right as you slide down the wall. You should completely avoid the first set. Now, the 2nd set is trickier - what I did was hung left and slid down the wall when the vertically moving spotlight was at it's peak. You should move downward at around the same rate it does, and if you hold left on the D-Pad, you'll continue falling towards the left wall once you reach the end of the first wall, and then it's just like the first set, very simple.

Now, just sprint to the end of the level. Don't be concerned when the alarms go off after defeating the 2nd miniboss - this is a scripted event and doesn't void the achievement. The achievement will unlock when you defeat the boss.