Undyne is at her core a person motivated by kindness. This isn't obvious at first, because of her extremely brash and aggressive personality, but at the end of the day her goal is always, always the happiness and safety of her people, her loved ones, and all those innocent or in need of her protection.
Kindness is not always a soft and gentle thing- as not only a member of the Royal Guard but it's leader, Undyne is prepared to unflinchingly defend the kingdom from any and all threats. Including- or perhaps especially- any humans that fall down through the Barrier. The Barrier can only be broken with the power of seven human souls, and Undyne has grown up knowing that they had six already, believing strongly in King Asgore and his plan to claim their power and free their people, taking the Surface back from humanity.
She hates seeing the way her people suffer down in the Underground, hates anyone being in pain when there's nothing she can do about it.
The only problem is... she can't quite stomp out the knowledge that humans are people, too. She tries very hard to, going through some fairly elaborate mental gymnastics to justify attempting to kill the player character and take their soul for the king, no matter how kind or cruel they've been in that particular playthrough, and trying to excuse her fondness for 'human culture' (read: anime DVDs and manga that fell down into the Underground from the dump, because even though she's badass Undyne is a complete nerd) by saying that she's studying the enemy to better understand a dangerous opponent, but at the end of the day? She knows that what they're planning isn't justice so much as revenge, inflicting pain on others as punishment for the pain they've endured. However much she stubbornly doubles down on her dislike of humans, refusing to admit to admiring them for fear of betraying her people's trust in her, she can't deny her doubts.
And once the No Mercy route comes around, she doesn't even bother with that- when she confronts the player character as Undyne the Undying, she outright states (correctly) that they're a threat to both humans and monsters, and that she'll fight them for the sake of the whole world, not just her own people. This is a noble realization, the willingness to put aside her old grudges and uncertainty in favor of truly defending all those in need, so it's a bit of a shame that even that wasn't enough to actually win that fight.
Other routes will show her softer side, if befriended- her love of cooking even though she's hilariously bad at it, her patience with Papyrus even when he's not terribly competent, her admiration for and raging crush on timid but brilliant scientist Dr. Alphys... but even in the heat of battle, her love for her friends is explicitly what motivates her, and her final words are that she trusts Asgore and Alphys to fight back against the player character, and save everyone despite her failure.
As the game puts it "she's loud, rude, and beats up anyone who gets in her way"... but she's also a hero. And she understand that it's a hero's job to fight for their people, no matter the cost.
Outside of battle, befriending her will reveal an excitable, melodramatic woman who loves, in no particular order, a good fight, a good meal, beautiful ladies, seeing other people get excited about the things they're passionate about, anime or literally any kind of fiction that involves hot girls with swords, and music.
In all honesty, Undyne can get pretty passionate about most things- if she doesn't already have a very strong opinion on something, give her five minutes to think about it and she'll be shouting on the topic soon enough. The fact that she's arrived here just after dying has knocked some of the wind out of her sails, but given a little bit of time to find her bearings and come to terms with the fact that she's alive again, and she'll be back to her old excitable self pretty quickly.
Re: REVISIONS REQUEST
Kindness is not always a soft and gentle thing- as not only a member of the Royal Guard but it's leader, Undyne is prepared to unflinchingly defend the kingdom from any and all threats. Including- or perhaps especially- any humans that fall down through the Barrier. The Barrier can only be broken with the power of seven human souls, and Undyne has grown up knowing that they had six already, believing strongly in King Asgore and his plan to claim their power and free their people, taking the Surface back from humanity.
She hates seeing the way her people suffer down in the Underground, hates anyone being in pain when there's nothing she can do about it.
The only problem is... she can't quite stomp out the knowledge that humans are people, too. She tries very hard to, going through some fairly elaborate mental gymnastics to justify attempting to kill the player character and take their soul for the king, no matter how kind or cruel they've been in that particular playthrough, and trying to excuse her fondness for 'human culture' (read: anime DVDs and manga that fell down into the Underground from the dump, because even though she's badass Undyne is a complete nerd) by saying that she's studying the enemy to better understand a dangerous opponent, but at the end of the day? She knows that what they're planning isn't justice so much as revenge, inflicting pain on others as punishment for the pain they've endured. However much she stubbornly doubles down on her dislike of humans, refusing to admit to admiring them for fear of betraying her people's trust in her, she can't deny her doubts.
And once the No Mercy route comes around, she doesn't even bother with that- when she confronts the player character as Undyne the Undying, she outright states (correctly) that they're a threat to both humans and monsters, and that she'll fight them for the sake of the whole world, not just her own people. This is a noble realization, the willingness to put aside her old grudges and uncertainty in favor of truly defending all those in need, so it's a bit of a shame that even that wasn't enough to actually win that fight.
Other routes will show her softer side, if befriended- her love of cooking even though she's hilariously bad at it, her patience with Papyrus even when he's not terribly competent, her admiration for and raging crush on timid but brilliant scientist Dr. Alphys... but even in the heat of battle, her love for her friends is explicitly what motivates her, and her final words are that she trusts Asgore and Alphys to fight back against the player character, and save everyone despite her failure.
As the game puts it "she's loud, rude, and beats up anyone who gets in her way"... but she's also a hero. And she understand that it's a hero's job to fight for their people, no matter the cost.
Outside of battle, befriending her will reveal an excitable, melodramatic woman who loves, in no particular order, a good fight, a good meal, beautiful ladies, seeing other people get excited about the things they're passionate about, anime or literally any kind of fiction that involves hot girls with swords, and music.
In all honesty, Undyne can get pretty passionate about most things- if she doesn't already have a very strong opinion on something, give her five minutes to think about it and she'll be shouting on the topic soon enough. The fact that she's arrived here just after dying has knocked some of the wind out of her sails, but given a little bit of time to find her bearings and come to terms with the fact that she's alive again, and she'll be back to her old excitable self pretty quickly.
After all, she's determined like that.