As an addition to what has been said before, here is my run playing solo/ full stealth on Overkill:
This also includes the 2 other achievements related to framing frame job.
Required equipment: Silenced pistol.
Required skills: Dominator and Smooth talker (mastermind tree), Cleaner (ghost tree).
Other skills from the ghost tree can help too (chameleon, shinobi).
If you have any questions, feel free to ask, I'd be glad to help.