You can unlock the weapons indicated below by satisfying the corresponding conditions.

Chrome Revolver - Successfully intervene in 20 crimes.
Destroyer Sniper Rifle - Finish 10 criminal convoy events.
Gangster Tommy Gun - Scan 17 QR codes.
Spec Ops Goblin Assault Rifle - Investigate all 9 weapon crates.
Wildfire Assault Rifle - Investigate 6 missing persons cases.