Dum Dums deal considerably more damage per second than any other weapon in the game. When tested, Dum Dums can reliably defeat the Battlelord at least twice as quickly as any other weapon or secondary ammo type. On a shot-by-shot basis, Dum Dums deal approximately twelve times as much damage as regular Pistol rounds. For perspective, this is roughly twice as much damage as a single rocket from the Devastator in Duke Nukem 3D. However, Dum Dums are relatively rare, usually appearing no more than once per level.
They are next found on Gun Crazy (known as "Red Light District" in Duke Nukem 3D) in a secret area behind the counter in the gun store. Opening the poster with "Riot Master" printed on it will reveal a secret compartment (Secret 3) with Dum Dums inside.
Duke-Burger (Secret Level)
Their third appearance is on the secret level Duke-Burger. Near the beginning of the conveyor belts inside the meat-processing portion of the restaurant, there is a column in the middle of the room. In the sides of this column, there are windows onto moving pistons, which are mashing up and down. If carefully timed, Duke can crawl through the pistons without being smashed and collect a magazine of Dum Dums inside the column. (There was a Devastator here in Duke Nukem 3D.)
The fourth appearance (or third appearance, if the secret level Duke-Burger was not found) is on Death Row. Specifically, they can be found by entering the secret area behind the bed in the jail cell containing the captive babe. Inside this secret tunnel is a pair of Night Vision Goggles, but the back wall of this tunnel can be opened to reveal an extended tunnel. The extended tunnel contains a magazine of Dum Dums.
After that, they can be found again on Toxic Dump in a secret area near the end of the level, but it will require explosives to access them. When you've reached the sewer tunnel containing a stream of toxic waste at the end of the level, ride the current roughly three-quarters of the way to the end. Around this point, you should be able to find a crack in the wall on your right. Blast through the crack and enter the room inside. On the other side of the column in the middle of the room, you will find some Dum Dum Rounds. (There was a secret exit button here in Duke Nukem 3D.)
They are later found on Launch Facility. After destroying the rocket ship near the end of the level, proceed down the elevator. In the room below, there is a switch on the wall that will open a path into the sewer tunnel. The Dum Dums can be found near this switch, behind a column.
Another magazine of Dum Dums can be found on the level Battlelord, before entering the door to initiate the boss battle. As soon as the level begins, quickly strafe to the left while Duke is falling in the air. If you're fast enough, you can land on a platform near the top of the column on the left side. The Battlelord will die after about 33 shots from the Dum Dums.