As stated in the trophy description, you must get at least one kill with each primary weapon in the game (including the DLC weapons) while playing as Insurgent class.
Insurgent class starts you off with just a pistol so the only way to get the weapons is to pick them up off dead bodies by pressing
This can make finding some of the weapons a little difficult as some are not so popular and are rarely used by other players.
Thankfully there is a bit of a workaround if you're struggling to get your last few. Simply spawn as the appropriate class with the gun you need and then commit suicide. Then respawn as an Insurgent and pick the gun up off your dead body and go get that kill!
There are 16 primary weapons and they are as follows -
ASSAULTLS36 Breacher
StA409 Keyzer
M55 Rumbler
LS21 Valk
StA25 Vlug
SUPPORTM82 Assault Rifle
StA59B Pulver
Vns12A Purger
VC30 Sickle
StA4 Stova
Pnv06 Voltage
SCOUTLS70 Fors
StA101 Kameraad
StA14 Rifle
LSR44 Spoor
StA61 Vultur