Going back to the Mahri Nui Arc, there were Matoran in Mahri Nui who were depending on bubbles of air forming which let the Matoran breathe in order to thrive in the underwater village. Furthermore during the ending of the Mahri Nui arc, Matoro sacrificed himself as well as teleported the rest of his Toa Team back to Metru Nui as his team were “breathing air.” This would imply that the Matoran as well as the Toa would have the ability to breathe. If that is the case, would the Toa be able to perform breathing exercises? If so, this could help them with their stamina as well as control the energy within themselves, such as the energy known as qi/chi/ki or something else. If this is possible, is there a way the Toa can tap into their full potential using their breathing similarly to the “Breathing Styles” from the anime Kimetsu No Yaiba? I have a feeling that something similar to the Breathing Styles could be a possibility to being a catalyst to some power being awakened but I could be wrong on this. If you have some comments to prove to be the case or contradict what I had stated, please discuss here and I will follow up with what you have to offer.
I think some of these question topics are getting a bit silly.
Every character in the Bionicle story has the ability to breathe, aside from mostly mechanical beings like Bohrok or entirely mechanical beings like Vahki. Greg has gone on record saying that because some MU inhabitants breathe, that means they are mammals, but that’s an aside.
Anime does not have correlation with other disassociated media in most cases, and Bionicle is no exception - there’s no evidence that breathing unlocks any kind of enhanced states or special abilities in the Bionicle world. In fact, there’s almost no powers requiring intense focus in Bionicle at all - most powered combat operates like a gun duel; it’s a matter of who pulls the trigger first.
And it’s better that way imo - I’m not exactly the most fond of anime, as other users can tell you.
I don’t think it is silly. I mean trying to exploit the biology of the Toa or Matoran is fascinating.
It can be fascinating, but we know almost nothing about the biology of any MU inhabitants. We can’t speculate the possible benefits of breathing techniques when we don’t even know why these beings need air at all.
I mean… it’s not like Greg has ever specifically said “Bionicle characters cannot use the Breathing Styles from Kimetsu No Yaiba”, but that doesn’t mean that they can, and it seems like a reach to assume an entirely new powerset when nothing like it has ever been hinted at.
You aren’t wrong, but what are you trying to exploit here? They breathe air, therefore they can unlock special powers? Real-life people can also breathe air, but breathing exercises don’t give us any special powers beyond some extra stamina and/or lung capacity. What would those special powers even be?
That’s not exactly true: while you are correct that Bionicle characters don’t really need any special “concentration techniques” to activate a power (assuming that they are physically capable of it, of course), it does take focus and/or willpower to master it, and the winner of two competing powers often comes down to which being has the greater willpower:
A few of Greg's willpower-based statements:
Official Greg Dialogue | Page 92
Chat with Greg Farshtey | Page 840
Chat with Greg Farshtey | Page 624
Official Greg Discussion | Page 14
Official Greg Dialogue | Page 93
Official Greg Dialogue | Page 156
Official Greg Dialogue | Page 157
Official Greg Quotes | Page 4
well, if you breathe loud enough, and fast enough, you get this super cool power of making everyone in the room concerned for your wellbeing
The only intense focus I can think of is Kapura’s teleporting due to his training. But to clarify for @Au-Plau-Se training and breathing focus isn’t an anime thing either but just part of eastern asian martial arts which anime pulls from.
I have no textual evidence to back this up but I think breathing is just like breathing for humans. It provides oxygen (or the Bionicle universe equivalent) for the cells (or the Bionicle universe equivalent) to undergo respiration and keep the organism alive.
I think something to keep in mind is that this category is for clarifying specific parts of pre-established parts of Bionicle lore, not for adding a completely new and albeit very random concept.
As people have said before the problem isn’t that it couldn’t be exist, it’s that it doesn’t. If you were drafting some sort of ‘what if’ fanfiction sure that’d be fine but this is the official canon story we’re talking about.
The Matoran and Toa are living right? I mean it is just similar to Star Wars. the ‘force’ resides in all living things, if that is the case, then there should be some sort of energy that resides in Matora, Toa, Turaga and Rahi as well right? Well this type of energy follows the similar principle as the “force” in Star Wars.
I think that a working application of this would be that a Matoran or other character could train to increase their focus or willpower through the use of breathing exercises. We do actually have a semi-canon example of this: in MNOG II, Hahli can breathe for a longer time underwater the more her Willpower stays are increased. This may just be a very specific, not-really-a-power application of @Au-Plau-Se ’s breathing exercises, but it is a realistic use of them that is mentioned in the storyline via a game that has been confirmed to be mostly canonical.
But would this make either the user who performs breathing exercises as well as in training, into Peak-Matoran-condition/Peak-Toa-condition?
Based on how I’ve seen these exercises used in the games, as well as in the movies and Greg’s stories, it actually could, or at least help them reach greater control over their current levels of power. In Mask of Light, Gali is shown to be meditating in the movie and novelization, while one of the Piraka does the same at the start of the Voya Nui arc. In both cases, they are doing this in part to control their emotions, but also to strengthen their focus.
There is a single example of achieving advanced power sets through meditation/mental discipline: accessing internal light/shadow. The Makuta of the prime universe and the Melding universe did this, purging all light/shadow from their being and enhancing their elemental powers as a result.
In addition, non-elemental species can pursue this as well: Roodaka is the perfect example. Her shadow blasts were a result of deliberately purging her inner light from her mind and body. She could just as well have done the same in the other direction, acquiring light bursts as an ability.
Arguably, breathing exercises could have been used to assist in developing mental self discipline, something required for the moral purge, but the breathing exercises themselves do not directly afford anyone a new powerset, any more than they would for us humans. Like Cordax summarized,
Yes… this why there is a Mask of Water Breathing in the very first year… 
I have to agree with the general sentiment here - What you are essentially asking is “Hey, can you validate/canonize my headcanon.” I’ll repeat these two lines:
Head-canons are 100% more than fine! However, it’s not necessary to run head-canons by the original author. If something isn’t mentioned in a story, that doesn’t mean it can’t exist. (Though, that it can exist also doesn’t mean that it does.) If you want to tell a story using your interpretations, no one would stop you.
‘Head-canon’ and ‘fanfiction’ have been kind of buzz-words, but I think it’s important to realize that all they really mean is that it’s not official. And even if you run every element of a fanfiction by Greg (which, don’t), the fanfiction itself wouldn’t be “official” - and that’s okay. It’s okay for us to tell our own stories. Even at that, it’s okay to diverge from what ‘canon’ says about the story, just as much as it’s okay to try to adhere to it as closely as possible. You set the rules for your own creation.
(Also, Greg hasn’t posted for almost half a year.)
Also in regards to focus – Many powers need you to maintain concentration 
Couple example quotes:
Yes
We don’t know that their is a force-like thing that resides in all living things in Bionicle
Assuming it exists, I suppose it could follow some of the principles, but obviously Bionicle characters aren’t interacting with it in the same way that a Star Wars character interacts with the force.
Again, I think you’re applying rules from other universes to Bionicle, with no basis as to why those rules would carry over.
You said that the characters weren’t interacting right? Well have you seen the Mask of Light? Takua slapped himself on his arm because of the bugs in the movie, meaning that Matoran and Toa would be able to feel. In other words they have a sense of touch or feeling. If one who is either a Matoran/Toa were to break his/her boundary to reaching new heights, there may be a chance to tap into this kind of power. Would it be possible?
ok we’ve already said this twice but let’s reiterate a third time
The problem with this theory isn’t that it cannot exist in the matoran universe, it is that it DOES NOT exist in the current established lore of the matoran universe and has never been mentioned
This category was made so that greg can clarify any questions that people may have had about the existing BIONICLE lore, not so that greg could add new parts of the story and create new mechanics for the characters to use.
Let’s also be honest, Greg is most likely not going to be answering further BIONICLE questions here.
Then you unlock the special teleportation jutsu where you wake up in a hospital bed