So, the easiest way to get this achievement is as follows:
1. Select "Local Co-Op Mode"
2. Have 1 player be Eli.
Now, after 2.45, Eli has a weapon that deals 0 damage, but knocks enemies back. You can use this to knock a slime into the second player, killing them.
3. Go into Zone 1.
4. Find a green slime.
5. Have the victim stand on one side of the slime.
6. Eli knocks the slime into the victim. They die.
7. And you're done!