You can do this in a private lobby.
The first 7 weapons the Slayer will have access to immediately. The 8th weapon, the BFG-9000, you can only get as an end of round upgrade at the end of the third round (going into round four.) This is a cumulative achievement; it doesn't need to be done in one match.
The recommended approach is to start with the shotgun and work your way clockwise around the weapon wheel (using
to open the wheel). Only the kill shot counts, so for example you could use the Chaingun to wear down someone's health then finish the player off with the Rocket Launcher.It seems that the BFG kills are buggy to register
. If you're finding the achievement isn't unlocking (and it only unlocks at the end of the match, not during the match itself), I would suggest getting up to two rounds of BFG ammo and killing both Demon players with two shots, or with one round of BFG ammo, get the health of both Demon players down very low and kill them at the same time with one shot.
Note that when you select the BFG as your round four upgrade, you only get one round of ammo. You can pick up at least one more round using the chainsaw against demons, but the ammo drop appears to be uncommon.