"You got to hit me harder than that, you pathetic animal!" -Undyne, in the Genocide Route
Undyne is an aggressive fish-like creature who is the former captain of the Royal Guard.
Undyne is a fish creature who has sharp teeth, combat boots, ripped pants, a tight fitting shirt, and a demonlike spear.
Her undying form is much different. It looks similar to her undying form in Undertale, but is more sharper and demonlike, hence her other nickname; "The Undying Demon".
Undyne is usually portrayed as deeply believing in Asgore's Words, and the general motto, "Kill or be Killed," and like Papyrus, shows no mercy to her foes. She is hotheaded and prone to fighting, only befriending Frisk if tricked into it, but otherwise not especially different from her canon Undertale counterpart. She has a good personality when she is with her crush, Alphys.
Some popular fan interpretations, usually those that coincide with making Papyrus the captain of the Royal Guard, have Undyne act rebellious towards Asgore's rule or, on the opposite side, weaker and more unsure of herself in personality.
Frisk: Undyne attempts to kill Frisk at first, but starts to question herself when they show her mercy. She then later, asks them out on a date and shows off her cooking skills. Because she is not good at cooking, it will burn down her house and get her mad at Frisk, which causes them to fight again. After the fight, Undyne realizes that Frisk is one of her only friends, so she stops fighting and gives them her phone number. In the true pacifist route she becomes a better friend with Frisk and starts calling them "little dude".
Alphys: Undyne and Alphys have a crush on each other just like in the original, Undertale universe. They hang out all the time.
Papyrus: Their relationship is tense, but they get along better than most monsters in the Underground. Undyne is unaware of the way Papyrus treats his own brother.
Sans: Being just his real boss. Stationing him as sentry duty while getting mad at him now and then for sleeping like in Undertale. She doesn't know about the way Papyrus treats him out of her sight. Undyne does notice his injuries and asks about them, but Sans would never tell her the truth, afraid of sabotaging her and his brother's relationship knowing that she could possibly be the only real friend his brother has.
Underfell Game Differences
This section is about the Underfell fan game by ManiaKnight. As the game is still in demo, some of this information may become inaccurate over time. And as this entire wikia is able for public editing. This information could just be from public opinion ;)
In the fan game, Undyne is "a problem" for Papyrus, suggesting she is rebellious towards the Royal Guard. "Some popular fan interpretations, usually those that coincide with making Papyrus the captain of the Royal Guard, have Undyne act rebellious towards Asgore's rule or, on the opposite side, weaker and more unsure of herself in personality."