With their enemies being as strong as they are, it's hard to believe that the heroes of Demon Slayer have survived any of their battles through the method of "breathing." Strangely enough, though, that is exactly what they have done.
The humans in Demon Slayer aren't normally born with special powers, unlike several other anime/manga. Aside from the occasional individual with a heightened sense, there are almost no "powers" to speak of for the humans of this world. Unfortunately, the series' demons have multiple powers such as regenerative abilities and enhanced physical abilities as well as their Blood Demon Arts, putting the human slayers at a huge disadvantage.
In order to close the gap between them and their sworn foes, the humans developed a technique called Total Concentration Breathing. When utilizing Total Concentration Breathing, Demon Slayers increase their physical and mental capabilities to their maximum levels by inhaling the most amount of oxygen possible while utilizing a specific breathing pattern.
By increasing the amount of oxygen in their bodies, the Demon Slayers can actually gain physical abilities that rival and even possibly exceed those of the demons they fight. While it does put a strain on the body, with enough training and conditioning even rookie Demon Slayers can master this technique to the point where they can maintain Total Concentration Breathing indefinitely, even while asleep. This is known as the Total Concentration Constant technique.
Total Concentration Breathing is the foundation of the Demon Slayer Corps' combat ability, but it's only able to be used to the fullest once applied to swordsmanship. There are many different Breathing Styles in the Demon Slayer Corps, each meant to be used with their own specific style of swordsmanship. In this way, many swordsmen have been able to create their own unique breathing and sword styles to complement their own specific abilities. For that reason, there are no "bad" breathing styles, just ones that are better for some than others.
It is important to note that the different Breathing Styles aren't magical in any way and are purely swordsmanship techniques. While it might seem like otherwise, especially when watching the anime, none of the elemental effects that are seen when the characters attack are actually there. Instead, they are meant to represent the "spirit" of the different attacks. Inosuke Hashibara's Beast Breathing Style perfectly illustrates this, as almost all the forms are pure sword strikes without being accompanied by some beastly image.
The different Breathing Styles are all derived from the original, Sun Breathing, but they were all inspired by different parts of nature. Zenitsu's attacks might seem to radiate lightning and create booms like thunder, but neither of them is actually present. His swordsmanship is just so deeply inspired by them that when looked upon it's almost as if his attacks are actual lightning strikes. For Giyu Tomioka's Water Breathing, there are no waves or water dragons, rather the stances are such that they make the eye "see" the essence and spirit of each strike. Even Tanjiro Kamado's Sun Breathing follows the same principle.
Speaking of Sun Breathing, it should be said that it is the most effective against demons. It may not actually create any flame just as Kyojuro Rengoku's Flame Breathing cannot, but the different forms as well as accompanying Breathing Style work in tandem to make each strike essentially feel like a slash from the sun itself, the only true weakness demons have. This specific style, especially when accompanied by a bright-red Nichirin sword, can harm even the strongest demons as well as hinder their ability to heal wherever they are struck.
While it is a little unfortunate that Tanjiro's attacks didn't actually create dragons of water and "Sunfire," it does help ground the Demon Slayers much more than if they did. It helps to illustrate the differences between the demons and humans as well as highlight why some humans, even Demon Slayers, might have felt compelled to be changed into demons. "Power corrupts" is a pretty well-known saying and in many ways, the demons of Demon Slayer perfectly embody that maxim.