Rocket Knight

As the achievement desciption very clearly states, you can't get hit by anything or fall down any pits for the duration of the level (Cyberswine Labs). You can however use Free Play/Level Select mode for this, and I highly suggest playing on Normal difficulty as well.
Also, any health pickups you get do not count against you or anything like that. It's not about keeping your health full, just about not getting hit at all.

The level is about 7-8 minutes long once you have it down, so it may require a lot of trial and error before you get the perfect run. One important thing to note is that while taking it slow is okay, you can actually run past almost all enemies on the level, which means you can avoid fighting the pig-walker things altogether. The only one I opted to fight was the one just before a checkpoint with a hangrail-operating switch, since it's a tight fit jumping over him. All the others can and should be easily avoided since they have platforms above them, although the very last one on the level requires a well-timed diagonal burst instead (he has rockets so don't fight him).
It turns out you can also just walk under them (between their legs), so feel free to do that instead for the last two unless you really want to dash or fight. Thank you to Virtuous Panda for that little bit of information!

The level is mainly focused around platforming past a lot of lasers, and there's little advice I can give here since it's all fairly obvious in how you're supposed to beat each part. Just be careful with your bursting, as it can be easy to overshoot into a laser in some parts.

Right after a room where you go up on horizontally moving platforms, there's a corridor with 4 pigs (two bombers, one gunner and one with missiles). Right at the start, stand on the ground and hit a bomb into the pig further ahead, then jump-hit the next bomb to take out the bomber. That gunner pig can be a real pain otherwise.

After the part where you go down a shaft chased by a horizontal laser, bursting from side to side, don't go up the wall ahead of you right away. There's a gunner pig and one of the little flying balls there, so jump up and go down again quick to lure the ball to you. Kill it, and then you can just burst over the pig. I got hit a bunch of times there, so I'm just throwing my method out there.

Also, for those balls, the burst vortex (the B button attack) is very useful, especially in the room where you have to kill a bunch of them at once.

Good luck, and if you have any questions about specific parts of the level, just leave a comment and I'll try to help! :)