Note: I've been writing my own solutions to achievements in this game. However, this guide comes from DaShAg, on the sister site - TrueAchievements.
Do note that if you missed some caps on your first playthrough and you are going back for them, the game won't save it until you hit a checkpoint !
Duke Lives
Mirror - Admire yourself in the mirror ( there are a lot of mirrors in the game but this is the first one you can get )
Toilet - Go pee, when you boot the game for the first time you are already peeing but that does not give you EGO.
Pool - Play a game of pool and pot all the balls, when you pot the white ball you will have to re-start unfortunately. ( Tip: You can press X on the cue ball when you aim at it anytime, it doesn't have to lay still. This way you can prevent scratch )
Damn! It´s late
Popcorn - In the lounge room is a microwave with bags of popcorn next to it. Pick up a bag and put it in the microwave.
Autograph - You will soon find a man with his son asking you to sign his book.
The Duke Cave
Dumbbell - Pick one up and do a curl.
Bench Press - First get all the extra weights and add them to the bench, after you've added them all do a bench press.
Punching Bag - Just punch it using RT
Basketball - Throw a ball into the hoop
Pinball - There are more pinball machines throughout the game, the highscore you have to beat varies with each player. You can check the backboard for your target ( credit to for pointing this out ).
Speed Bag - Like the Punching bag, just punch it.
The Lady Killer
Slot Machine - Pick a slotmachine and keep playing until you win. On the machine itself you can see what combinations you need.
Vegas in Ruins
Beat the boss
The Duke Dome
Copy Machine - I like this one, go to the copy machine and make a nice copy of your ass :)
The Hive
Walltits - Give 'm a good slap
Queen Bitch
Beat the boss
Duke Nukems Titty City
Glory Hole - On the men's toilet, hahah I love this one
Stripper - Tip a Stripper ( on the little stage with the pole, the stripper will eventually walk to the end of the stage where you can tip her, if there is no stripper on stage, try going backstage and back to the stage again )
Porno Movie - There is a room in the strip club with a key lock on it. The code is "4768". Now pick up the porno DVD you can find there and put it into the tray of the DVD player.
Alien Abortion - beat a game of Alien Abortion
Poker - Win a hand on the poker machine.
Air Hockey - Win a game of Air Hockey
Crash Course
Frisbee - After you climb up, you'll find a sportsbag, a ball and a frisbee. Pick up the frisbee and throw it.
Duke Burger
Cigar - In the beginning of the level, when you arrive at the duke burger turn around and walk over the snake-like thingy. Eventually you'll come across a reception desk, go trough the door and you'll find your cigar in there on one of the shelfs.
Pornomagazine no.1 - Find in the toilets at the beginning of the level
Mighty Foot
Binoculars - There are multiple of these that look across the canyon. Look for those things you also see at let's say, the Statue of Liberty.
Computer - Close to the Binoculars is a security building, get on the roof to access it and use the computer for some porn.
Ghost Town
Pornomagazine no.2 - When you get to the church get out of the Car and into the church, you'll find it somewhere hidden under a broken bench.
Dam
Beat the Boss
Paper Plane - After the boss, walk up and you'll find a schoolbus. The paper plane is in the back of it.
Shrunk Machine
Calendar - After you got the Freeze gun you'll come into a larger room, head for the double doors. Walk in and turn around, the calendar is next to the doors. Browse through all the pages.
Forkstop
Pornomagazine no.3 - At the start, the first room, on one of the shelfs
Generator Room
Beat the boss
Blowing the Dam
Beat the boss