Just setting the record straight considering I just got this.
Okay, so first you want to keep a lookout for blue doors. They are always close to merchants so whenever you find a merchant, look at your map and see if there are any blue dots close to your position. I really only saw one of these doors that could possibly be missed but assuming you are exploring every nook and cranny of the game (like you should be) you can't miss them. The first one does not become available until you are in Salazar's castle (chapter 3). So if you are freaking out because you haven't found any, you're probably still in the village.
To get a bottle cap you MUST have 3,000+ points. Don't know why people are saying 2,000 but they are wrong. The only exception is with rare bottle caps where you must either score 4,000+ points OR hit all targets.
To do this, shoot the targets (duh) and gain points. Body shots will give you 50 points while head shots net at least 100. If you get five hits in a row (combo) the back of the range will open up and a Salazar target will move across the rear window. This is worth 500 points so get it if you can. Hitting it also counts toward your next combo.
DO NOT hit Ashley targets no matter how much you hate her. If you do, the game will penalize you 1,000 points. Good luck recovering from that.
Everyone seems to say "TMP, TMP, use the freaking TMP." I disagree. The TMP will be your mainstay weapon but it is not the end all solution. There are five I got with the pistol, including the last two which were the most difficult.
I managed to get three bottle caps from game Type A with this as well as the last two in Type D. It has advantage in the fact that it is only semi-auto for more controlled firing but it seems that no matter how much you've been using the handgun through the game, Leon becomes inebriated once he walks into the range so accuracy and control leaves much to be desired. It can also be problematic for taking out the bonus Salazar targets and considering the recoil, you'll need to adjust your aim after every shot or your accuracy will drop drastically. Not much of an endorsement but if you practice you'll get the hang of it.
This will be the mainstay, so like it or hate it, you will be forced to use it the most here. I recommend playing through the game with this thing to try and get a feel for it, but you don't have to. The reason this is your choice weapon is because of its magazine capacity, and the fact that it's steadier than the handgun. The disadvantage comes with the trigger sensitivity. Only the lightest of trigger pulls keeps this thing at a one-shot firing rate and even then, it will occasionally double-tap, eliminating your chance at a bonus target and possibly killing an Ashley target when she starts to make her appearance. In the last Alternate Game Type you will have better luck ditching this one altogether as it will hit so many Ashley targets that you will be throwing your controller. In the meantime, though, might as well get comfortable with it.
Don't use this weapon... Ever. It's good with accuracy and stability, but the spread means that you will never get a combo going.
The only time I really used this was on the last two bottle caps and it was in tandem with the handgun. This is the most accurate weapon but it suffers from slow firing rate, the need to cycle a round after every shot, and the time it takes to get into the scope. I recommend against using it except in the case of the last two caps.
1) Take It in Stride: Some have said that this beast of an achievement can be put off until the fourth firing range located on the island and then done all in one sitting. Do yourself a favor, don't do that. The game's frustrating enough to not have to sit in the same spot for hours on end trying to cram all of this in like a procrastinator in finals week. Every time you find a door, play the game and get all six bottle caps. Then you can space the achievement out, feel like you're making progress, and have some fun in between the aggravation. That, and completing a game type give you money to spend, so it helps in the game as well.
2) Go for Rare Caps First: First thing you do when entering a range is to play the game newest game type and focus on hitting all the targets to unlock the rare award. Don't worry about accuracy, or combos, or quality shots; just kill them all, but don't hit the Ashley targets or it won't count. The reason you do this first is because after three regular bottle caps the game type will offer an alternate, and more challenging, setup. It is best to get this one out of the way before that happens. In addition, it helps you re-familiarize yourself with Leon's drunken aiming, and you can get an idea of how the targets come up.
3) Take a Break: You've spent hours doing this and only have a handful of caps to show for it. It might be one, two, or three. But now you're tired, frustrated, and can barely get a measly two grand. You know what I do? Leave. Collect your caps, save the game and then turn the game off. You'd be amazed how you can improve just by giving yourself a day away from this grind before going back to it. It certainly helped me.
4) Make a Barrier: It's so frustrating, and you just long to get back to the regular game. Maybe if I just progress a little and then come back to it- DON'T DO IT. This is the kind of thing where you just need to knuckle down and say "I'm not continuing until I get this done!" Force yourself to finish the game type before moving on. This will help with tip #1.
5) Go for Perfection: Okay that's a little drastic, but if you mess up (hitting an Ashley target) and you know you won't be able to recover (hitting an Ashley target) spin around, walk up to the doors and exit. The game will ask if you want to leave the range. Hit yes and the game will reset, saving you time.
6) Find a Good Spot: I've seen video of people running back and forth along the bar and they're just making it harder for themselves. Find a good spot (experiment) and stay there for the duration of the round. This will help you avoid having to memorize complex sequences of when to fire, when to move, etc. The only time you need to break this rule is on the final two caps.
7) Manage Targets: On close to medium range targets, go for head shots, unless you know the chances of making it are slim. Distant targets should really only have body shots as they are more guaranteed hits, but feel free to go for the head if you think you can make it. Some targets will also disappear faster than others. Memorize these and shoot them as soon as the chance arises. For fast moving targets, aim a bit in front of them and wait so that they come to you. If a Salazar target drops, screw everything else and grab him. He's worth 500 points so it's worth losing one or two targets to get him.
8) Experiment with Weapon Loadouts: Don't go crazy. Each time you switch out it takes a bit to get used to the new weapon. If you find yourself getting frustrated, though, try switching and putting in a few rounds with the alternate weapons, it may be the difference you need. If worse comes to worse, practice with the handgun and then when you're half decent, switch to the TMP and the extra accuracy may be the boost you need.
9) The Last Two Caps: The alternate Type D game is traumatic. Ashley pops up everywhere and only a few real targets are hidden in her midst. In this case I used the Sniper loadout, using the handgun for regular targets. Once you rack up enough hits for Salazar to drop, swap for your sniper, and shoot him. After the hit, slam the start button until it brings you into the inventory, and switch back to the handgun. Remember to be patient. It pays off more to get combos then to be fast or get head shots. Using this technique I managed to get at least 3 Salazars (possibly 4) which equates to 1500 points. The rest should take care of themselves. Finally, this is the one game type which requires you to move. Don't worry, though, you'll only have to move from one side to the other. It's just that at certain angles some targets aren't visible. I recommend starting to the left of the bell and then when the set comes where you can't see any targets, move to the right and you should be able to make them out. Hit them then move back and you should be good.
Well, that's all the advice I really have except to be patient and keep at it. Good luck. If you have a critique, let me know.