This is a real simple challenge and too me three rounds to obtain playing solo.
Usually I play coop, but I chose solo as it's better to set your enemies up.
First things first, these are double executions not coop executions. You just need to kill two enemies during the same execution . It can be done solo.
The only thing you want to aim for, is trying to get everyone your fighting (or at least two) ready for execution. When the skulls are above their heads, make sure they are close to each other, then execute with RT. If you have positioned them correctly, the execution will involve both enemies. However, sometimes it goes wrong, and you'll end up doing a single.
Play solo on courtyard, and use focus to set up easy executions.
When I got mine, if I was surrounded by say eight enemies, I'd use focus until I had all eight ready for execution without killing any, then wait for one to attack me. As he comes in for an attack, I'd execute. This always resulted in a double execution for me.