If she came from a heavy gravity environment, then to a lower Earth gravity, it would allow for the dexterity here.
This was also the Golden Age explanation for Superman's powers.
Some of these suggestions will work better or worse depending on exactly how "super" you want the character to come off.
I will warn that I'm coming more from the perspective of somebody who writes in the setting, as opposed to somebody who's role played in the setting. So, I don't know how these will work in a system game or anything like that... and I'm taking things like "weaknesses" and "tension" into account, more on instinct than anything else... I don't know how much those things will be desirable to your character creation. But, I think they can also be overlooked in most cases, if you didn't want to worry about that stuff.
Sometimes you get perks for taking weaknesses in your character creation, though, right? >.>;; I don't know much about table-top gaming... sorry...
The power set you're describing are essentially the same powers that Captain America has (my personal favorite super-hero), though I don't know if you mean them limited to the same degree.
Essentially somebody either with her knowledge or without her knowledge wanted to create a weapon to serve function X as part of agenda Y. Through either selective breeding or genetic resequencing (depending on the tech-level appropriate for your story) a "perfect" living weapon is born/made. Depending on the level of technology available in your setting you can get away with this being anywhere from just an "above human limits" level (like aforementioned Captain America) all the way up to "super" levels.
Also, you could combine this with Kazyth's nano-machines idea to come up with all sorts of combinations. And depending on the origin of the character how they came upon these powers says a lot about who they are and what their role is as a superhero. Were they like Captain America and elected to undergo this procedure? Or where they like X-23 and literally a product of the experiment?
This works best if it's just a "beyond human limits" set of powers. But, you could go the Iron Fist route and have had the character simply trained to a substantial degree in mysticism and martial arts. Through years of training they've reached a level of battle meditation that has surpassed the limits of a human body. This plays into your original idea of "energy manipulation", too. They can focus chi through their body to amplify their strength, speed, stamina, whatever you need. Putting their chi through their skin they could make it as hard as stone to resist damage.
You wouldn't really need to explain away the agility or dexterity in this sense, either, since it's unlikely somebody spends that much time learning some magic martial art and doesn't leave the practice fairly limber.
Arguably, you could go the Dragonball Z route and let your imagination run wild with this and say that they've surpassed human limitations so much they can punch through mountains or whatever. But, it really has to fit within the setting. If everybody around you is Iron Man or Wolverine, and you're Goku-level... it stretches verisimilitude. Things should remain internally consistent within their own universe.
I wrote a character in something of mine that had beyond olympic level strength and stamina and while he didn't really have a resistance to damage, he didn't feel pain like other characters. In his case it was because his body produced adrenaline in insane levels all the time. He reacted faster than other characters, and he never stopped coming. But (and this is one of the reasons I really like this one) it came with its own weaknesses, as well. He had to regulate his heart-rate through drug therapies; basically he was hooked up to the opposite of the thing Bane has in Batman comics. And because his body was constantly in an "alarmed" state, he couldn't sleep which lead him to suffer from paranoia and hallucinations and extreme mood swings.
But, basically everything that a human body does is regulated and controlled by our biochemistry on some level. But this one's not going to let you stretch it too far beyond reasonable disbelief.
In the comics (at least during the 90's, they've gone back and forth on the matter since then) Bane's super-human level strength came from a drug called "Venom". The nice thing about drugs in a comic book style setting is that you can generally get away with saying they do whatever you want them to do to your character. In Bane's case they worked like a super-steroid that caused his muscles to balloon up like Broly from DBZ and made his skin super-tough. You could say that your character takes something that gives her all the abilities you're looking for.
Like the previous one, this one is nice because it adds its own weakness. If the substance she needs is addictive than you can have withdrawals for the character, and you get to play around with the ethical question of somebody destroying themselves in such a way in order to help mankind (since she's not using the powers for evil, right?). You can probably push this one a little further than the normal range of disbelief... but if there's an injection that somebody can take that turns you into the Mighty Thor, you're left with the question of why everybody's not taking it. So, there's things to consider before using this approach.
The character found, created, or was chosen to be the heir of some technology that allows her to do these things. The suit would handle all the questions of things like agility, strength and durability. But say you don't want a suit, there's no reason she can't have a ring that puts an amplification field around her body that works in all the same ways as a suit or whatever. For example, Superman's modern explanation (well, pre-New 52, anyways) was that his powers came from the aura around his body. It wasn't actually his muscles that were strong, it was the aura around the muscles, a microscopic thin layer of energy that his cells emitted because of yellow sunlight. So, your character could have a ring or necklace or an implant that allows her to summon up the same kind of thing. To the casual observer it would look like she's taking a shot-gun blast to the stomach and shrugging it off, but in reality it's the invisibly thin aura taking the shots for her.
You get lots of cool aesthetic options with this set-up... like the Mass Effect holo-armor and omni-tools. And, if you need it, you have weaknesses programmed into this origin as well. If it's a tech suit, then she's a normal person outside of the suit. If it's something like a ring, you can add a limited charge... maybe it only works for an hour before it needs to recharge, for example. Forcing the character to be selective about when to use their powers is often a good way to amplify tension if that's part of the goal. The biggest positive here is that you can literally go as far as you want with the powers... it could be a minor boost she gets from the tech, or it could turn her into the Silver Surfer. It could also come with its own costume like the way the Green Lantern's or Sailor Moon's powers work... never under-estimate the benefits of a quick-transformation ability.
Expanding on what Kazyth said. She (or, if you want to add a limitation, somebody else) either puts a series of enchantments or runes on their person or artifacts that she can wear. Again going back to something I wrote... I had a fantasy setting with a white mage character. His companions made fun of him because he was a white mage that only knew extremely low-level healing spells. He'd focused all his efforts into learning status boosting spells. He wore a charm that allowed him to cast up to three spells at once, and when his opportunity came, he would cast status boosters on himself (the story-equivalent of haste, atk up, and def up) and basically run around the battlefield like a fantasy setting Juggernaut.
Depending on how you set it up, you can use this one almost interchangeably with everything I said about the alien tech idea. Maybe there's a limitation on how long the enchantments can last... maybe she does't personally know how to replicate the enchantments... if the enchantments are on artifacts she wears instead of on her personally, then they can be taken away and used against her. Also, you can still get the quick-transformation costume with this... Shazam/Captain Marvel is the most prominent example that I can think of of a magic-based hero with a quick change.
So those are what I came up with...
Also, it's worth noting that with something like agility/dexterity... depending on your character's origin, you don't really need to "explain" where that comes from. Nightwing from the Batman comics is pretty much the most agile guy in the entire DC Universe and it's not from a super-power, it's just from growing up as an acrobat. In most super-hero settings, a character being able to do flips and high jumps and stuff is pretty much expected of them.
I'm not saying you can't or shouldn't have it part of their power set... but, I mean, if you want them to be really agile but can't think of how to work it into a particular power set... just say she does Yoga a lot, or something.