I found out that you can actually start up solo lobbies and do acheivements that do not require kills due to you being completely alone.
At main menu click "Create a Game" then choose the map you desire, so for this achievement it is "Kitchen Run".
Then down the bottom of your screen, Tick the "invite Only" button and press "P2P" this will take you to a lobby and you can just press "Force Start Timer" and away you go :)
Simply run to the other side of the map (extremely easy is the map is linear) and reach the cup and the achievement will unlock