METAL WOLF CHAOS XD

NOTE: This is not my solution, this was originally posted by another user who has since been removed, not sure if they removed this solution before getting removed themselves or what, anyways this was a very useful guide for me. I was able to retrieve this solution using the Wayback Machine for this page.

This is actually the hardest achievement in the game. While most weapons can be unlocked by either investing in their specific categories or finding weapon drops in-game, there's 14 weapons that can only be unlocked after you beat the game, and achieve an S rank for various game stats. These game stats are for all levels overall, and only count your best run for those specific categories. The S-Rank requirements are:

Total Clear Time: Under 45 minutes. Unlocks the Laser Assault Rifle BR.
Ammo Used: Under at least 2,200 (my count was at 2,041 when I unlocked S-Rank) Unlocks WRE-RH, Richard's freezing revolver.
Alien Capture Time: Under 15 minutes. Unlocks a Ray gun.
Collateral Damage: Cause at least $350,000,000 in damage. Unlocks the CRAC shotgun, which fires confetti.
Total Points: Over at least 5,000,000. Unlocks the multimissile launcher HANABI, which fires firecrackers.
KO Points: Over at least 1,600,000. Unlocks the ELEPH flamethrower, which shoots bubbles.
Damage Taken: Over at least 2,200,000. Unlocks the Railgun DRG, which fires dragon-shaped tracking rounds.
Tread (Stomp) Kills: Over 700. Unlocks the sniper rifle BB, which shoots baseballs.
Projectiles Intercepted: At least 1600. Unlocks the SHARK missile Launcher, which shoots Shark shaped rockets.
Destruction (Chaos) points: At least 16,000, it goes hand in hand with the financial damage score. Unlocks the grenade launcher AFB, which fires american footballs.
Chain Combos: At least 550,000. Unlocks the machine gun G-BOW, which fires arrows.
Rush Combos : At least 400,000. Unlocks the TAIHUO, a cannon that shoots cannonballs that explode after a few seconds.
Hostages Rescued: Gotta save 'em all. Unlocks the MLS (You know it's a FromSoftware game when you can get the Moonlight Greatsword.), which acts as a bazooka shooting out an energy blast with lightning strikes.
There's also a revolver (GRE-RH) that you unlock fairly quickly into NG+, but I'm not sure what that tracks. Perhaps money or resources earned, but it's not something you have to go out of your way for.

So, getting these S-Ranks range from "You should unlock them immediately on NG+" to "Several playthroughs of levels in order to get the perfect run". I'll give a few tips on what I found:

General Tips: You're going to want some pretty good guns when going after Total Clear Time and Ammo Used. For these, the final sniper rifle you unlock through investing (SC-RH) is fantastic. It's ammo used for each shot is 10, but that's one hell of a lot better then the couple thousand you'll burn through otherwise. You can also skip the charge time between shots by pressing cn_B twice after shooting. In addition, the final machine guns you can unlock (MG200/EN, MG200/ST, GG-RH) can shred through enemies and target buildings. Using all of these in tandem is key. Also, if you unlock any of the above weapons, you can use them for clearing the other levels. I've found G-BOW and MLS to help a lot with the clear times.

Total Clear Time: Despite the fact there may be multiple target buildings or bosses left, several missions can be completed without blowing them all up or even beating a boss. For example, the alcatraz mission ends when you get into that central area and blow up the batteries there, regardless if there's still buildings standing. Likewise, Phoenix and New York end as soon as you beat the mini-bosses there, and Miami ends after blowing up the boat. The toughest missions to beat for time are going to be the boss missions, Liberty Island, Las Vegas, and the Space station. The SC-RH helps a lot here, as it always does a bunch of damage to the bosses, and the MG200/EN and MG200/ST are great as well. My end score was 32 minutes, so you should have some breathing room to get it under 45 min.

Ammo Used: As I mentioned above, the SC-RH hits like a tank, and only counts as 10 ammo per shot. Using that, along with your stomp move for the target buildings, can really help bring down your score. Also, the SC-RH has penetrating shots, so if you line up right, you can take out multiple targets at once. Much like the clear time above, you can find out which targets/bosses you need to beat for a level, and only focus on them. Biggest ammo draws are once again going to be the bosses, and with an overall score of 2,200, this one is going to be the toughest to get done.

Alien Capture Time: After beating the game, you'll notice an alien icon pop up on some levels. That icon means there's an alien on the level, and you can shoot down it's UFO and then shoot the alien to capture it. The timer goes from when the mission starts, and it's pretty easy to blast it down with machine guns. I'm not sure if an S-rank is needed, or if you just need to capture all the aliens to get the gun. In any case, make sure you complete the mission after capturing the alien, which is a little tricky on Liberty Island.

Collateral Damage: This will be one you'll unlock almost immediately. If not, just go into a mission and blow up everything you can and finish it.

Total Points: For the first white house mission, and really any mission with infinitely spawning enemies, you can kill them over and over again to increase your score. Once you hit a million points on a mission this S-Rank is basically guaranteed.

KO Points: Another one you'll unlock almost immediately, if not doing the above strategy for total points should boost you enough to grab this one.

Damage Taken: This one is a lot trickier. For this one, you'll need to be careful as you go through the levels to not take so much damage. Again, this one is probably the worst on the boss missions, but using SC-RH and staying at a far range can help a lot. All else fails, use your machine guns to shoot down any projectiles. If you can do this on the final boss, you'll unlock another achivement and be well on your way to grabbing this S-Rank.

Tread (Stomp) Kills: While at the white house, take some time out from shooting the infinitely spawning soldiers to stomp them instead. If you keep going to 1,000, you'll unlock another achievement.

Projectiles Intercepted: Get your machine guns and head to the Grand Canyon. Once you meet the mini-boss, let him fire his missiles and shoot them down. He fires a bunch at once, and you'll practically be able to get the S-rank off this mission alone.

Destruction (Chaos) points: See Financial Damage above.

Chain Combos: So, back at the white house and all those soldiers. Using a handgun with a lot of ammo, you can shoot these guys one by one and not have to worry about accidentally blowing up their spawn copter. if you get around 10 100 combos in, you'll have this one in the bag.

Rush Combos : Rush combos are when you blow up a target or enemy vehicle in a very short amount of time when you first engage it. You can tell when you get a rush combo, as it says COOL or NICE. The white house mission (again) spawns trucks which you can stomp in one hit to kill them to get a COOL score. Also, at Miami, the bombers there also spawn indefinitely. Utilizing some good bazookas (TWBZ, TWBZ-RH) and some good timing, you can shoot a lot of these guys down.

Hostages Rescued: I'm not dedicated or clever enough to list all their locations in the levels, but keep an ear out for their cries of HELP!, and remember to always use light weapons when destroying boxes, because you never know. Also, in Beverly Hills, check the rooftops, and in the northwestern area, shoot down the garage door with Metal Wolf Chaos on it. Oh yeah, and in the grand canyon, in the last place at the very top, turn around and look at the top of the structure.