A warrior must be relentless in his pursuit of victory. They must never give up.
Samurai Champloo isn't and never claims to be historically accurate. The show makes it very clear at the beginning of their first episode. One thing that the show is true to is to never surrender when possible. Real Samurai would often commit Seppuku(ritual suicide) to prevent capture, and modern soldiers have POW training that tells them what to do when captured by the enemy. It does not include giving into their captors. In both cases, the attitude of a relentless warrior is embraced, and the brutal character Mugen is practically an embodiment of this fierce philosophy. You can't hear it, but he just told his would-be executioner that he would rather die then gravel toward him. That did not make him happy.
A good solider and determined warrior always finds a way out.
One things soldiers are told to do and what Mugen is a natural at is always looking for a way out. It's always option B, C, D, all the way down to & if possible. What POW manuals do teach is to organize and look for a way out. A way to escape without giving away information or giving into their captors torture. As Mugen can all too easily demonstrate, even a soldier with his hands tied behind his back can be lethal.
No matter what you see on TV, they never come one at a time.
A popular myth in both anime and other forms of media is that when in combat, you can take on one bad guy at a time. In real life, as demonstrated in Samurai Champloo multiple times, even Samurai don't dare make the assumption that their opponents will fight fair. Real combatants can do and will do everything in their power to overwhelm their victims. Fortunately, both Mugen and Jean alike are well equipped to take on multiple assailants. For all is fair in love and war, and Mugen is all too willing to take on the world.
Always keep moving, and train to do so.
For dangerous combat situations in real life, the best and first option is always to escape. The U.S. Navy Seals are the best trained soldiers and secret agents in the world. They are among the most fit and the most deadly and would gladly recruit the likes of Mugen or Jean. Their training method is ruggedly efficient; combat training and cardio. That's it. They run a half a mile from one punching bag to the next. Not unlike Mugen in this gif here. Being able to escape in a real fight give you a 96% chance of survival, even if your opponent is armed with a lethal firearm. Thus it makes sense to always be on the move and always be ready and fit enough to run away and live.
If running isn't an option, take cover.
There are generally two kinds of cover when it comes to live combat. One is hard cover, which can protect you from deadly projectile attacks as well as help you hide. The other is concealments, which does nothing to actually block an attack, but does make it impossible for anyone to target you. Stay as low as possible while moving.
Disarm if not execute your opponent as quickly as possible
If running or hiding is not an option, it falls on the person defending themselves or attacking to remove the target as a threat. The most effective way is usually to kill them, but a very good substitute if that is not an option is to disarm them of their weapon. Mugen takes this advice all too literally.
One Man. Any Weapon.
The greatest riflemen in the world are the United States Marine Corps. They say the above slogan to remind themselves that the deadliest weapon can often be a sick imagination. The owner of that hand is very lucky that Mugen didn't decide to go for the throat.
Always have a backup plan
As was mentioned before,the first option should be escape. While Jean takes a rather innovative approach to this, in real life having a plan B is as easy as knowing your exit points and identifying cover and concealment. Jean makes both by smoke bombing and running. Most people would have better luck remembering which way the doors are and understanding that iron, steel, and concrete objects make the best cover. Aluminum cars usually only offer concealment unless you can hide behind the engine block.
Always have a backup weapon to go with said plan.
While concealed and open carry laws vary from location to location, soldiers and shogunate alike always carry a backup weapon. Be it a pistol and knife, a Wakizashi sword (Samurai short sword), or a cleverly concealed dagger, having a weapon to fall back on in the heat of the moment saved more lives then either side of any war could count.
The first defense is to be alert. Always.
The best sword or gun or dagger or martial arts training will not help anyone who isn't paying attention. Jean can attest; being aware of your surroundings is the best way to survive any dangerous situation, especially combat. There are people a lot more vicious and ruthless then even Mugen, and being unaware is usually how they end up hurting innocent people. Such victims usually survive when they are alert. Then they extend their ability to survive by escaping, hiding when surrounded, and fighting when cornered, in that exact order.
Real combat is a brutal, ugly thing. Even anime as good as Samurai Champloo do not provide definitive answers to emergency situations. However, there is a kernel of truth in every piece of media consumed, and this anime is unusually rich in such details.