Simply kill 100 monsters. You should get this automatically while playing the game.

Unlock the first sniper by buying it in the armory. First go to the sniper section in the armory (marked in picture 1/left picture), then buy the sniper (marked in picture 2/right picture).

Destroy five cars. They appear in the first level. This should be no problem, if you are having better equipment.
But it can of course be done even with the default weapons. All you need to do is let the car pass and you can spray it down with the Rifle/SMG that you initially get (credits for this hint belong to Buttskie).

Simply finish the game by completing all missions. (You only have to kill some specific opponents to get further. You dont have to kill all of them. You can simply go ahead through the level.)

Buy the last German Rifle. Therefor you need 5000$ and have to reach level 8.First go to the German Rifle section in the armory (marked in picture 1/left picture), then buy the Rifle (marked in picture 2/right picture)