Every Psychopath boss fight from the walkthrough, compiled here for quick reference. Each one links back to the day it's fought on if you want the full surrounding context.
Encountered on Day 1.
When fighting Carlito there are 2 really easy strategies. If you grabbed the Katana you can get up right next to him and slash him 2 times and he'll go down — don't worry about taking hits, you'll survive, just go head on and slash him till he drops. Of course, if you have the Mega Buster you can just launch shots at him from a distance and you'll have him down even quicker.
Encountered on Day 1.
Go up the left side stairs and over to the Space Ride. If you don't have the Mega-Buster, continue past the Space Ride and grab some handguns from the police. If you have the Buster don't even worry. If you have to use the handguns, the best strategy I find is to stay a decent distance from him and wait till he blows up a balloon. Right when he throws it, unload some shots around his knees to destroy the balloon and damage him greatly and make him cough. While he's coughing, unload more shots into him. Rinse and repeat. If you have the Mega-Buster just go nuts on him and he'll die quickly enough.
Make sure you get a photograph of him if you are going for that achievement.
Encountered on Day 2.
Now you have to lend David a shoulder, so do so and make your way as best as you can to the "Huntin' Shack" (N127). Clear out the zombies in front of here and set a waypoint for David to hang out at. Enter the Huntin' Shack and you'll meet Cletus. Once again, easy to kill with the Mega-Buster, but doable with any gun or the Chainsaws — just look for when he reloads or takes a drink to do the most damage. Make sure you grab a photo of him at some point too.
Encountered on Day 2.
You now have to fight sniper Carlito — blast him with the Mega-Buster, force your way up close to him and chainsaw him, or grab some hockey sticks from the second floor sports store and go to town on him. Not a very difficult fight, just gets annoying when he shoots you and knocks you down.
Encountered on Day 2.
Head back to the pharmacy, and when you get close, Steven will appear. Make sure you get his photo and watch for his shotgun attacks. Any ranged weapon will take him down moderately well, but you can also sneak up behind him and chainsaw him pretty easily — not too tough if you just stay out of his way.
Encountered on Day 2.
You'll have to fight Cliff here — he's kinda crazy, but just like all other bosses in this game there's really not much strategy aside from having the right weapons and killing him before he kills you.
Take a photo of him sometime if you need to, and after you defeat him you'll get the Empty Room Key.
Encountered on Day 2.
Now you have to kill Jo the Cop to get her survivors. Time is running low on "Another Source," but Jo will begin to kill off her survivors if you wait any longer to do this scoop, so be as quick as you can killing her and freeing all her survivors. Photograph Jo if you need to.
Note: if you really can't do it and don't feel like retrying, skip Jo for now and continue back to the security room with the survivors you have. You can let 3 survivors die and still get the 50 survivors achievement — Jo has 4 survivors with her.
Encountered on Day 2.
Time now to head to the North Plaza to take care of some Girl Hunting. When you get over by the grocery store you'll have to fight Isabela — your best bet is any type of firearm so that you can hide in the middle circle area. You can kill her with the Mini Chainsaw in about 2 hits, but often you'll find that when you swing at her it just goes straight through her if she's not in the perfect spot to be hit.
Encountered on Day 3.
Take a photo of Sean if you need to and hack him down with your Chainsaw — he'll fall plenty quick. Now, before worrying about the survivors, head to the back of the theater and take care of the final group of cultists that is slowly making their way in. Once you've cleared them, you're done dealing with the cultists!
Encountered on Day 3.
Enter "Casual Gals" (W102) to find Paul. You can easily kill Paul before he even attacks you once, but make sure you get a picture of him before doing so if you need Psychopath photos. Paul is special because after "defeating" him he is no longer a Psychopath, but turns into a survivor! However, you have to be quick to save him. Grab the nearby Fire Extinguisher and do your best to spray it on him — this is the reason I say to definitely save before doing this, since sometimes you think you're spraying him and apparently you're not at all.
If you spray him enough, though, you will put out the fire and Paul will join you. Now take a picture again to get him as a survivor. If Paul dies you HAVE to reload to get him — he's not just a dead survivor, he'll cost you the Transmissionary achievement too, because he has a special call later.
Encountered on Day 3.
At this time you'll have your final showdown with Kent — he is now officially a Psychopath and you will need to defeat him. So get your photo of him and take him down. With him is the survivor Tad, whom you can save once the battle is over.