Outland

You can probably get this from the start, not sure if there are 20 enemies before the “flashback” to the future (Look at comments, and read TVthePunisher method for gaining this achievement earlier than my solution.)

Otherwise it's fairly easy to get in the City world on The City Walls map. It's right after you have beaten the 2nd boss. The reason for this is that you will get your Beam Attack here, and right above the place where you get it, there is a lot of flying jellyfish (around 12). At your convenience there is also an Energy Crystal, so you can charge up the Beam Attack endlessly (this is the best place to get the Overkill achievement too). Move further up to the next checkpoint – it's right besides a big blue shield soldier.

Die so all the enemies respawn. Then let the big blue solider get you down to 1 heart pounding heart. Get back to the checkpoint on the right, kill the 2 small soldiers before you jump over the the big one – from the ledge besides the checkpoint – and start backtracking down to the Energy Crystal, killing (almost) everything on your way back down. Save your Beam Attack (you should have 2 energy bars at this point) for dropping down and attacking straight away, and for killing flying foes. When I had beam killed all the flying jellyfish at the Energy Crystal, I still needed more kills. So I did a bit more backtracking to the left, beamed a blue flying jellyfish, refilled energy and did a drop down to the moving platform, beamed a red one – and one more soldier form the big group below the moving platform.

Beware of health hearts dropping down on you, especially at the Energy Crystal where you beam attack a lot.

I got this during the Golem boss fight. Get His health low enough so he starts to smack the tree and drop the bug looking things. (Make sure you have only one heart as well.) They die in one hit and all you need to do is avoid his shockwave attack. Make sure you don't get the Golem's health too low or he will start attacking with light and dark energy from the sky.

Once you work out the pattern you should get the achievement with relative ease.

I did this after I had nearly beaten the game, but you can use this method as soon as you obtain light energy. This method should be easy because all the enemies are neutral, and will die with one hit.

Backtrack back to "The Story Begins" get down to one hit point, and then you can kill however many enemies you can, try to get at least 2 or 3.

NOTE: When at 1 health enemies will drop health very frequently, you must avoid it, or you will need to restart. When I did this I made sure to avoid the health, rather than destroying it, if anyone can confirm this working with destroying the health I will edit the guide.

After this go right to "Origin: Rites of Passage" and kill the enemies in this level, there should be 18, locations are listed below.

You should see 6 spiked enemies running on two separate blocks very soon in the level. After that jump to the right, above the top ladder and you will find 2 spiders. At the bottom of the ladder there will be another 2 spiders, one at the bottom, and another to the left.

Drop down the chasm and you'll find another spider, near the diamond blue lights. Keep following the path to the right and you'll hit a checkpoint, and at the bottom of that drop will be another spider. Drop and you'll find another 2, one at the left of a slide spot, and another to the right when you jump up. Go back and slide down and there will be another spider. Keep following this path and you should find 2 more.

Next you'll have to backtrack back up and slide under 2 sets of spikes and then through a small opening where you will find 2 more spiders.

You should be able to get 18 kills in "Origin: Rites of Passage" if I counted correctly.