This season 7 week 1 quest requires you to collect different weapon types. This basically means you need to pick up 5 different weapon types.

You can find weapons all over the island. You can get them as floor loot, from chest, supply drops, cosmic chests or drop eliminating other players. This quest should come naturally as you are bound to encounter at least 5 weapon types.

You will need to pick up 5 of the following 8 weapon types:

Pistol

Submachine gun

Shotgun

Assault Rifle

Heavy Assault Rifle

Rocket Launcher

Rail Gun

Pulse Rifle