Do kills from Runic Mines raise the kill counter

I built supply depots at the bottom of the ramp, and made them sink into the ground. Then I created a line of marines for him to kill, like a cookie trail for him to follow, then told them all to "stop" (so they wouldn't move). With about 50 seconds left, I sent a single reaper to lure the brutalisk to my cookie-trail of marines. When he got below the ramp, I put the supply depots back up.

The lava doesn't kill him right away, but the marines damaged him enough that he died before he could make it back.

According to this post, "In sworcery mode left click and hold down on a lagomorph for a few seconds and it should explode"

According to this video guide, you don't need to go anywhere new to find the lagomorphs that you need to kill. The two lagomorphs you indicated are all that need to be found in order to complete this achievement as they can be respawned by leaving and returning to the area. The process is very simple:

1. Kill both lagomorphs.
2. Exit to another screen and return to see the bunnies respawned.
3. Kill both lagomorphs. You will get a message after the first.
4. Exit to another screen and return to see the bunnies respawned.
5. Kill both lagomorphs.
6. Exit to another screen and return to see the bunnies respawned.
7. Kill one more lagomorph. You will get a message.
8. You could try waiting and see if it pops, but in the video guide, although the poster was unsure if it is needed, they exited to the main menu and that's when the achievement appeared for them so it may be necessary to exit to the main menu once the killing is complete.