Ecco the Dolphin

The Death Sonar is obtained by helping out the dolphin in "The Vents" level (there's a respective achievement for that, so I won't go over the fine details).

To perform the Death Sonar, begin a dash (with X) and press B (for sonar). If this sonar hits an enemy, it will deal damage. Some enemies are damaged more by this attack, so learn to use it well! Add to this the fact that it's "ranged" and that Ecco somewhat compensates for your aim, the game becomes a bit easier. The thirty enemies will come naturally if you use this move consistently from here on out, especially when dealing with the small and large crabs.

As a small side note, you can actually get pretty good at this as long as you limit the time between pressing X and B. In other words, pressing them in quick succession will prevent Ecco from dashing at all, and the sonar will still shoot out. This will help with control.

If you want to get this achievement right away, it's easy. Given the (lazy?) scripting of the game, most enemies respawn the second you're one screen away. Simply find a cluster of jellyfish, kill them, swim one screen away, and they'll respawn. Since they usually come in clumps of three, you just need to do this ten times!