Let's start with some basic's, my beloved 3 ground rules:
1) Pause the game
Pausing the game will allow you to: spare yourself of a great variety of grave and deadly mistakes. By pausing you can give your crew order's that will be executed immediately, and it'll be the difference between a landslide victory, a Pyrrhic victory or your shipwreck.

2) Verify the opponents weapons
How you do it?
Check the image bellow.
By putting your mouse on the sections icons you can see what weapon they have on each section. Why? It's simple: every weapons has its gimmicks, the one on the image above, it's the flamethrower, its range is limited to Short and boarding proximity, so, if you don't want to play as firefighter and lose, keep the ship away. By discovering what weapons your enemy have you can minimize the damage you'll take and the cost of the repairs.

3) Pay attention to the enemy's water level!
This is a habit that usually takes quite some failures to get, but i hope that with this warning you will manage to avoid that.
But actually i don't think you will... at least not until you sink, unintentionally, 5 ships
You must pay attention because one of the purposes of the killer's way is to kill the crew without sinking the ship, which would lead to a decrease in loot and the loss of possibles supplies and the failure in the acquisition of the ship's plants. And I'll repeat this a LOT so pay attention... please

First and foremost: this guide isn't for beginners.
This guide assumes that you already have some understanding of game mechanics that I didn't cover in the basics, like the composition of the crew and the weapons layout and other stuff.

There are two ways to play the Killer's Way: the Sinker and the Killer.

The Sinker, as the name states, aims to sink the enemy's ship quickly in order to minimize the damage received while sacrificing part of the loot and the supplies, it sacrifices profit for clearing speed.

The Killer, obviously, aims to kill every single member of the enemy's crew and capture their ship, which often takes time, but by doing this you'll obtain the entire loot and possible supplies, which can lead to damage to the ship, injury and/or death of the crew in the initial stages, things that will increase your expenses in the ports.

But the path is not reduced to the choice of weapons, it extends to the way you play the game, the piracy system in this game, is particularly "unadvisable" most of time, since once you accumulate 2 or more skulls you will be hunted by bounty hunters.
With 3 you'll won't be able to use any ports, this will force you to find a way to reduce your wanted level back to 2 skulls, since you wont be able to repair your ship do note that, the norm of the Bounty Hunters ship's is to be stronger then yours. Unless you already have a full fledged Man' O War, in this case just kill them all

All this translates as you facing a series of tough battles of attrition, since the damage will accumulate until you pay the authorities your fine 500 gold coins more or less .
But there's hope! There's a way around this, since piracy in this game is really profitable, the method i developed haven't seen it in any other guide or being spread on discord, so yeah it's MINE is simple:
Attack the trade route to the edge of the second skull, like in the image bellow and stop:
This will earn you 300 coins, and keep the ports open so you can go to the magistrate and deliver a crew member to them, he'll go to the jail and you're free to repeat the process.
It seems contradictory to exchange crew for money since you'll spend money to hire new ones, but remember that you can get crew by saving castaways and investigating lifeboats, so it's always good to "open" a space when you see their symbols, and it's a worthwhile investment if you stick to the cheaper ones you'll pay 65~90 while raking a net profit of 200 coins at bare minimum.
Furthermore, there are valuable traits to have in the crew such as:
The Fast Learner - gains 50% more experience.
The strong Fist - will not be knocked off the ship
I'll only list this two because i think they are the most useful ones, so if you saw a Gunner or a Striker with a Fast Learner trait I'd say to the unfortunate traitless healer: useless scum out of my way! Mister Magistrate, yor honor this is the criminal take him away.Do realize that in the early and middle stages the skill level of the crew wont have a big impact in the fights. That's why you're free to make them pay for your crimes, even more so if you're at the beginning of the main campaign and still don't have a good ship and your crew is a mixture of healers and sailors and you haven't been to the Imperial Port, by activating the crossing gate you will receive a full pardon, clearing your pirate status, so before that: Go and plunder at will!
You SHOULD keep the FL crew members, but why preserve crew members whose traits are basically useless?

Let's start with the Sinker:
The Sinker's path is the easiest, the least stressful, and least demanding, armed to the teeth with his mortars he forces the enemy crew to drop their weapons and run to fix the holes opened in the hull.
You'll be using the Heavy Bombarding configuration of 6 mortars, although you can change their number allocation i'll heavily emphasize that this composition sinks faster:

3 Hull Crackers yep it's portuguese, my mother language, you can pv me for grammatical errors

Pros
[1] Will cause at least 2 cracks, normally 3 or 4 cracks.
[2] Will delay the loading of the enemies weapons and halting their offense since at least one of them will depart to fix them.
[3] It may kill when hitting a crew member in red health.
[4] Fills the water bar quite quickly.

Cons
[1] It's slow.
[2] Does little damage.
[3] Wont kill anyone by itself.

2 Ship Smashers

Pros
[1] Will cause a "Brace For Impact" event, temporarily paralyzing the enemy crew.
[2] Will delay the loading of the enemies weapons and halt their offense during the BFI and after it since one of them will have to drop the weapon to fix the crack.
[3] It can kill when hitting a crew member in red health.

Cons
[1] It's slow.
[2] Does some damage.
[3] Will take quite some time to sink a ship.

And 1 Ghost mortar.

I recommend the GM, since it will spawn 2~3 zombies, and don't underestimate them, three of them can easily put any crew member on the yellow, you should put the drop area at the helm or in the infirmary, on the helm they will make the navigator drop the helm allowing you to approach more easily, on the infirmary they will attack and maybe kill the ones making use of it, depending on how much hp they still have.
It can also be the Acid Bomb, normally when using it I place the drop area on the cracks that are being repaired to stall for time, and to lower the hp of the repairing individuals are dead man even individuals? or in the infirmary to stop them from healing themselves.
You can also go full Hull destroyer but i wont recommend this comp, since it will take some time and you'll take quite some damage depending on the enemies ship's weaponry.

Pros
[1] It's Fast & Furious baby depending on your crew artillery skill.
[2] It causes a huge damage to the ships hull.
[3] Deals some serious damage to the crew.
[4] Will kill If it hit a crew member on the red health.

Cons
[1] Will cause a single crack.
[2] Wont cause a "brace for impact" event paralyzing the crew.
[3] Wont ever knock someone off the ship.
[4] Heavily relies on your crew skill level.

With this we conclude the Sinker's Way.

The Killer's Way is more demanding in the sense that it requires your constant attention in battle, as a Sinker it's enough to determine the target of the mortars and let them sink the enemy's ship, there is no need for a large and constant number of commands.
But a Killer must always be aware of what is happening in the enemy's ship, in order to: minimize the damage received, increase efficiency in eliminating the enemy's crew, acquire the entirety of the loot, possibles supplies there's no guarantee they'll drop, but the drop rate is acceptable and acquire the ship's blueprint.For that the best weapon layout is the Strike
Why do you ask? It's simple, this weapon attacks directly at heart of the problem: the enemy crew. Without causing damage to the ship, which reduces to zero the chances of an accidental shipwreck, losing part of the loot, all the supplies and the ship's blueprint, the killer's way brings all pros and fewer cons.
Here I will introduce the two main paths of the Killer's Path and they are the Berserker Killer and the Lightning Killer.
Berserker Killer.
The weapons of the BK are 2 Berserk Dart Guns, 2 Snipers, and 2 mortars If allowed by the ship
As the name implies the strategy revolves around the Berserk Dart Gun and the Sniper Gun. And it's quite simple: always aim the BG at the crew member with the highest level of melee skill, do realize that the marines wont always have this skill maximized, you'll see many healers-killers outperform them in this aspect. Keep the shots of the sniper for the ones whose HP have fallen to the orange level, 2 shots of the sniper can kill anyone on that state.!!!!!WARNING!!!!! WARNING!!!!! KILL THE HEALER FIRST !!!!!WARNING!!!!! WARNING!!!!!
Ships with 3 or more healers will give you a migraine
At the start of the battle look for the crew member with the highest level of melee skill and use it to lower the HP of others while using your snipers to end their lives, note that, here your mortars will be important to kill them quickly.
Once again I recommend the GM, and now I present to you his little sister, Miss Spider Eggs, this duo of summoners will keep the enemies struggling to decide how to die and without time to load and fire their weapons reducing even more the damage received by your ship. It's important to realize that this pair of siblings do not get along, so don't put their drop area in the same section! My recommendations are to put GM drop area on the helm and the spider's on the infirmary, since eventually a orange spider will spawn and upon death will create a small acid area similar to the one created by the Haliphrons.
Since we are speaking of the devil, I'm gonna give you some tips, when facing the cult it's a GOOD and WISE idea to use your first shots of BG on them, but you don't need to worry if they survive or if you miss the shot, there's a trick to deal with them in case you fail to kill them before the board your ship. Get to board distance and shoot wich mortar is ready (only works with GM or Miss Eggs), or both, and make the crew member fighting the Haliphron, move somewhere else dropping the fight with it, as soon as the zombies and/or the spiders spawns they will jump back to protect their ship, now just use the BG on them and get your helper back in your slaughter party.
Another option is the Acid Bomb and the time-bomb in the place of Miss Eggs.I wont recommend the Ship Smasher because you do not want to loose the seconds of insanity for a failed impact preparation.
With this we conclude the Berserker Killer's Way.
Lightning Killer
The Lightning Killer is a tad more quick and easier than the BK, all you have to do is to hoard them end kill them, the level of damage you'll suffer will depend on your skill, more precisely in how capable you are in grouping them before lighting them up.
The strategy remains mostly the same, but now you do want to have them clustered and laid on the floor, so your Lightning Gun and your Acid Bomb may hit them all hard and lethally. This will require a great deal of skill, since you'll want to hit them when they are agglomerated and half a second could lead to a different result, the Ship smasher can help by making them fall on the floor, so back to the basics: PAUSE THE GAME!Now i don't recommend GM and Miss Eggs, for the simple reason that they have a pitiful quantity HP leading to a single lightning, killing the former and heavily injuring the later, but since they are consumables fry them if you want, what matter is to kill the enemy. It's also a good idea to keep a Sniper in the beginning since it isn't easy to hit 3~4 guys with the Lightning Gun.