Defense Grid 2

The first level to contain any of these aliens types is level 06 (There are Rumblers).

Notes -
I've seen reports of level 05, though when I replayed it on a seperate account, I didn't get the achievement.
I also replayed level 06 on a seperate account, and the achievement didn't unlock, though I know Rumblers are on this map.
Level 07 is the first with the actual BIG aliens, so that may be your best bet.
At any rate this achievement seems buggy or the criteria isn't right. It should unlock somewhere in the second page of levels at least.

Practice mode (and most other game modes) seems to give the level the same wave setup, so practice mode on easy difficulty would probably be the easiest way to get this.
I don't have really any specifics on tower placement, I could go into it more if people have trouble.
I prefer to focus on cannons as the bulk of my force. I used to use guns quite a bit but have found cannons tend to have better payoff. I try to put tesla towers near the beginning if I have too much trouble with shielded enemies.
Practice mode starts you with 2500 resources, while the normal level starts you with only a couple hundred, so you should have no trouble on practice with just about anything you could possibly build.

If you have trouble specifically killing the boss aliens, just use General Cai's ability and it will kill it instantly.

As with all other achievements in this game, this achievement will not unlock until you finish the level.