From The TimeSplitters Wiki

Blunderbuss
Ammo	1/100
Fire Rate bullets per sec/cartridge time	1 bps, 100s
Reload Time	0.8s
Damage (per Single Shot) Head/Body/Leg	100%/100%/40%
Type	Shotgun
Zoom	No
Primary Fire	Fires similarly to a shotgun
Secondary Fire	Same, only wider burst.
Games	TS1

The Blunderbuss is more of a novelty weapon than a serious killer, but it can be used quite effectively in certain circumstances. The weapon only has one shot per reload, and the reloading takes ages, but that shot does a lot of damage to the enemy because two shots is sometimes enough to kill them. The best way to use the Blunderbuss is to blast an enemy, and then run away. As he follows you, you should reload, turn around, and blast him. This will usually kill him, if your shots were aimed in the right direction. If you simply shoot an enemy and then wait for your weapon to reload, this will usually give him enough time to turn around and gun you down, so this is not advisable.

Shown left is the Blunderbuss when equipped. You get an opportunity to use this weapon in Tomb, but I would advise against it due to your alternatives of the Mauser Pistol and the Tommy Gun.