If you're at least A+ strength and fighter skill and wear an Aketon, have a decent armor and a top-tier weapon, it is possible to win many of the Fogs battles without potions. Roundhouse Kick and Battle Cry work with all weapons, but the other six techniques require one of crushing/slashing/piercing weapon type. So learn the techniques that work with your favorite weapon.
Battle Cry and morale damage in general is less effective in the Fogs because enemies recover morale at a rate of half the damage they do to you (same for you in reverse). Weapons that only do morale damage are the lash, the whip and the cattle prod. These are for subduing slaves (you might get lucky with them in the Fogs but it's unlikely).
Battle Cry gives you Fury (2x red damage buff) which can combo with Roundhouse Kick (ideally when Enemy also has red Unsteadiness debuff and is defending with red Blocking stance). Roundhouse Kick is always a red attack but the damage type depends on the weapon you are using. However Battle Cry doesn't do any damage so if you have another way to get Fury, it's often better to use the other way.
To win battles you need to minimize your damage taken while maximizing your damage done. Your defensive stance leaves you vulnerable to one attack color so check it every round and if necessary change it according to your buffs and debuffs and the enemy's buffs and debuffs to minimize your exposure. Also pay attention to how hard they hit with each attack color, sometimes they use special attacks that do more damage of a specific color. Without potions, focusing on offense tends to be a better strategy, as you only have a few rounds before they will inevitably kill you. You need to stack buffs on yourself and debuffs on them to increase the amount of damage you do, with the goal of using a special attack color that gets a 2x multiplier from your buff and a 2x multiplier from their debuff and a 2x multiplier from them using the defensive type which is vulnerable. In total, 2x 2x 2x = 8x multiplier, which is either a killing blow or close to it. If you can't get an 8x multiplier (depends on luck for the enemy to choose the vulnerable defensive type), at least try to get 4x (buff + debuff).
If a particular enemy usually has an Adrenaline defensive buff or applies Weakness to you, then your red combos will be weaker. If your weapon only does green and purple attacks, then it will work better against enemies that don't focus their buffs and debuffs on one of those colors.
That's the basic concept, the details are up to you. Practice in the arena with your weapon of choice.
To maximize your chances, you can use different weapons depending on the enemy you're fighting (conceptually, you go to the Fogs with a specific weapon and you patrol until you find the "right" type of opponent; in practice, save before you patrol, see what you get, reload your save, swap your gear, patrol to get the same encounter).
A few of the weaker enemies have a 100% chance for your attacks to miss unless you have at least a 2x multiplier agsinst them. The "scum" encounter is an example of this.
