This should give you enough time to get up and behind the wall to avoid detection. 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. Once you've done this, use the walls as cover from the spotlights.
Using charged shots followed by regular buster shots, take out the enemies patrolling the area. You'll know you've touched one when the screen flashes and a siren goes off. In order to do so, you must not touch any of the spotlights seen in 2 sections of the level. (Thanks to Shi Kiseichu for the PM of this!) Here is a password that takes you to the next boss as Magna Centipede, to make things easier. 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.
(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). You cannot return to the stage after defeating them to unlock the achievement. NOTE: Must be done on the run where you kill the boss.
