Yes. Trophies can be unlocked by a group or in solo.

It's normally best to buy all weapons by a group to unlock this trophy, to achieve this trophy effectively, follow this method:

 - Be fair when opening doors, each player should take turns to spend their points when opening doors.
 - Be prepared to gain many points before going out to buy all weapons.
 - When ready to buy all of the weapons, use a grenade on a group of zombies (when near to end of a round) and make them legless which will leave you precious time to save running around to buy all weapons (including you and your friends/team mates to spend points towards the doors).

You may need about at least `10,000` roughly to spend on doors, and at least `12,000` to `15,000` (from what I remember ages ago). 

The Collector trophy does not require upgraded weapons or weapons from the mystery box.


----------

This may be quite hard to achieve unless you have a good motivation of escaping and surviving from a large swarm of zombies and also taking them down, be sure to make good use of your grenades for high points when used against a swarm of zombies!