Here, things get a little more challenging. Throughout the level, there are two main kinds of robots you will encounter - ones that look like flying light bulbs, and green ground-based ones that shoot out a fireworks-style explosion when killed. Killing the bulb bots causes the lights to go out, but killing a ground-based one restores the lights. Because there are a lot of bottomless pits in this stage, I don't recommend killing the bulbs. You need to see where you're going at all times. Simply dodge the shots the bulbs fire, and don't return fire unless you have no choice.
At some points in the level you'll encounter small platforms on a half-circle railing. There are two kinds - red and green. Red ones will break off when they reach the opposite end of the railing, while the green ones will stay attached, and repeat the course. Take this into consideration when navigating the level. If you beat Drill Man first and got the Rush Jet, it will ease the pain of these sections considerably.
There are also sections across a spiked pit, over which you must ride grasshopper-like robots. These are tricky sections, just be sure to get off the grasshopper at the right time. Rush Jet (if you already beat Drill Man) can make things a lot simpler.
Bright Man himself can be a pain. His primary method of attack is stopping time, and unloading on you with shots from his own arm cannon. You'll want to shell out the acid rain you got from Toad Man to melt his circuits. But even with his weakness, he can still be a threat. Dodge him as much as possible. You WILL get frozen in time, so be sure you get frozen in a situation where his shots won't do you as much harm. Hopefully you got the Energy Tank earlier in the level; it's insurance if you aren't able to beat him with acid rain alone.