This is by far the worst achievement in the entire game.
Here are some tips to help you.
-EDIT: I got some things wrong whilst writing this guide, some corrections have been made, but the people in the comments have given a lot of good advice if you're still stuck, glhf

Welcome to Hell


Proving Grounds 1
Enemies are only harmed by weapons.
Make sure to get the two gun users before getting the rest of the enemies.
Whenever you're downed, dodge far so that you don't get stunned.
DO NOT PICK UP THE CANON IN THE BEGINNING, you can't drop it after picking it up.
Take a small weapon and then swap to canon nearer to the end of the battle

Proving Grounds 2
You're stuck in Beast Style, so make sure to use as many items as you can to deal the most damage,
The enemies will gang up on you, so be quick.
Grabbing an enemy and then using a heat action does a lot of damage, so do it often.

Proving Grounds 3
No matter what you do, you'll complete this one
Use it as a chance to have a somewhat enjoyable fight in such an annoying and frustrating section of the game.

Proving Grounds 4
Basically the same as 1, except a lot easier as there's no gunmen. Just focus on building heat and unleashing heat actions on as quickly as possible

Proving Grounds 5
4 waves of Zombies will come at you.
Dodge and run as much as you can and try to keep a lot of distance between you and any zombies.
Zombies don't stay down for long, so take them down and use a heat action quickly.
This one takes a while, keep trying and you'll get it.

Proving Grounds 6
You need to get 30,000,000 yen in two minutes using Breaker Style.
This one is also extremely annoying.
Focus on building heat, you get more money with a higher heat, and make sure you don't use heat actions unless necessary, as to stop you from losing the heat you've built up.
If you get hit, you might as well alt+f4 and go again.
Light-Light-Heavy attacks will carry you through not only this battle, but throughout the achievement.
Get used to pressing x-x-y

Proving Grounds 7
You have to break boxes on mannequins and get 30,000,000 yen in two minutes
This one is pretty bad, but quite easily done.
First prioritise getting rid of the mannequins with guns. Whilst going round the Perimeter to get all of the Gun Mannequins, destroy the biggest boxes you can see. Easy W

Proving Grounds 8
This is the worst one out of all of the Proving Grounds.
There are 4 groups of 3 enemies, and your health is constantly draining.
All of the enemies aren't especially difficult to deal with, but make sure to not get careless and take unnecessary damage. Feel free to use lots of Heat Actions, they stop your health draining whilst the cut scene is playing.

Proving Grounds 9
This one is not that bad.
8 enemies throughout 4 groups are trying to kill you, and if you take any damage, you die.
Your main focus should be separating each group away from its other members, then getting rid of them as quickly as possible to make the other members scared and hesitate to attack you.
The first four should be easy to deal with.
For the third group of people, knock down the Fat Guy first, then immediately get rid of both gunmen, which shouldn't be too hard. By the time the Fat Guy gets back up, you should be able to focus attack him.
For the last guy, grab a bicycle and go to town

Proving Grounds 10
This one is also not that bad.
8 enemies throughout 4 groups that are trying to kill you, and if you take any damage, you die
Again, your main focus should be separating each group away from its other members, then getting rid of them as quickly as possible to make the other members scared and hesitate to attack you.
The first 4 are also manageable for this challenge.
For the third group of people, get rid of the guy with the shotgun first, then get rid of the rest. For the final guy, learn his actions just before he throws his fans, and then dodge very far

Out of the 4 of these different types of Climax Battles, you might think that this is probably the most enjoyable, as it goes back to the most fun aspect of this game, the fighting, but don't be fooled. This is brutal. So, here we go.

Melee 1
This one is easy. All you need to do is destroy a bunch of people within 90 seconds.
Kiryu does a lot of damage when he has full heat, so build up your heat quickly and don't use any of it on Heat Attacks until you are right at the end of the climax battle.

Melee 2
This one might take a while.
You need to K.O 3 rounds of people within 90 seconds.
Heat Actions do a lot of damage to opponents and stop your timer from going down, don't be afraid to use them.
Throws will also be very useful.

Melee 3
This one is pretty easy.
There are 3 waves of enemies, you just need to K.O them in 90 seconds.
First six are fine, the last 2 are a bit worse, but nothing that can't be dealt with.
Just get used to side stepping and dodging and you'll be fine.

Melee 4
Again, 3 waves of enemies that have to be beaten within 90 seconds.
Side Stepping and dodging will once again be your best friends.
Build up heat and on weaker enemies and then use heat actions on the stronger ones. This one is pretty bad, get ready to do a lot of replays.

Melee 5
This one is less difficult, so use it as a nice break from the torture.
60 seconds to K.O 3 waves of enemies.
Immediately pick up the chair for the first wave, target the shotgun guy first for the second wave, and just fight through for the third

Melee 6
90 seconds to K.O 3 waves of enemies.
Use Light-Light-Light-Heavy attacks to build up heat and deal a lot of damage.
Save up Heat Actions for more difficult enemies.
The first wave is the hardest, deal with it as quick as you can and you'll be fine.

Melee 7
This one will take a toll on your physical and mental health.
If you are using a controller, consider switching to keyboard and mouse for this segment, you'll be more accurate.
This section requires very, very good timing, but once you get it down, there's no way you'll be able to fail.
As the game loads up, start turning around.
Once the game starts, attack the enemy with a shotgun directly behind you.
Get him down as quickly as possible, take his shotgun, then mash Heavy until all enemies are down.
Get ready to retry this one a lot.

Melee 8
If you've finished Melee 7, you'll find this one way easier.
As the game starts, pick up the canon on your right behind the barrels.
Mash Heavy Attack and you win.

Melee 9
This is the easiest out of all of these, and you have plenty of time.
150 seconds to get rid of 6 people.
Kiryu will do a lot of damage at max heat, so build up your heat and keep it high.

Melee 10
Another easy one.
150 seconds to get rid of 6 people.
Use either Slugger or Breaker, I personally used breaker because of the leg swings.
No matter what you choose, try to focus on one person and build up your heat quickly.

Just a couple of Mr Shakedown fights. You can do it, I believe in you.

Millionaire Battle 1
Just fight Mr Shakedown.
That's it.
No Caveats, just skill.
Build up heat and do damage.
Easy W

Millionaire Battle 2
Same thing as the last.
Just fight Mr Shakedown.
That's it.
No Caveats, just skill.
Build up heat and do damage.
Easy W

Millionaire Battle 3
Beat 10,000,000 yen from Shakedown within 90 seconds
Your main goal here isn't to K.O Shakedown, but to get money from him.
Dodge behind him with Rush Style and throw as many punches as possible.
Build your heat up and don't use any Heat Actions, Kiryu gets a lot of money at max heat.
If you get hit once, start over.

Millionaire Battle 4
Beat 30,000,000 yen from Shakedown.
This one is easier than the last.
Build up heat as quickly as possible, switch to Slugger and use a Heat Action.
That should give at least 25,000,000 yen, you can get the rest relatively easily

Millionaire Battle 5
Two Mr Shakedowns. At the same time. Good luck.
Stick with Brawler, and do your best.
Focus one before trying to attack the other.

Millionaire Battle 6
Same as last time,
Two Mr Shakedowns. At the same time. Good luck.
Stick with Thug, and do your best.
Focus one before trying to attack the other.

Bosses in succession, with 10% health recovery between battles. There's a reason that this is the Ultimate section

Ultimate Battle 1
Okabe, Oda and Kuze. In a row. Oh boy...
Use brawler.
That's the only advice I can give.
This and Ultimate 2 are the hardest fights out of all of these, so once you do it, you'll be in good stead for the rest

Ultimate Battle 2
Lee, Nishitani and Sera.
You can destroy Lee with Slugger, Nishitani with Breaker and Sera with Thug.
Get used to dodging and get used to mashing Light-Light-Heavy, it'll carry you through this fight.
This and Ultimate 1 are the hardest fights out of all of these, so once you do it, you'll be in good stead for the rest

Ultimate Battle 3
Nishitani, Lee, Sera, Awano and Kashiwagi.
Enemies do less damage, but still be careful.
I used a mix of Brawler and Rush, but you can use whatever you want.

Ultimate Battle 4
5 sets of Kuze, one from every Kiryu-Kuze fight.
Thug, Slugger or Breaker will work fine, just use whatever you're best at.
You might need to do a lot of restarting for this one.

Ultimate Battle 5
Oda, Kuze(2), Awano, Dead Puncher, Sera, Kuze(5), Nishikiyama, Kashiwagi, Shibusawa and Lao Gui.
You get the point by now, use whatever you feel comfortable with and lay hell down on these losers

Ultimate Battle 6
Awano, Dr Kirihito, Sera, oda, Yoneda, Kuze(5), Lao Gui, Kashigawa, Nishikiyami
This is your last climax battle.
Have fun with it, throw in some heat actions, you get the drift.
I would use Brawler, but do whatever you want, I trust you

That's everything.
Thank you for reading, hope this helped