Red is a child-monster (she's a poodle), adopted into the Royal Guard. She wants to kill the player in order to implement a plan that Asgore had created to destroy the Barrier. Having heard of the friendly relationship between the Guard Dogs and the player, she feared that the player would try to befriend her, she decided that she will do everything in her power to stop them.
Edgy kid Red wears a grey cloak instead so she doesn't get spotted easily, but her Deltarune symbol is red (like Toriel does). She still has her bow-tie and looks harmless, but all of a sudden she chops you in half with her katana. She has a red glowing eye (like Sans) which gets red each time (That's is a energy bar when it goes white) she has Asgore's blue-orange thing, but way more faster.
She has two sides. Her first side is a sweet harmless girl which gives out (poisoned) muffins (sounds familiar to muffet, eh?). When they know she's too nice, they've most likely already become a pile of dust. She acts fast as Sans dodges. She always obeys Undyne and Asgore's commands.
Despite a supposed lack of hatred towards human kind, her initial interactions with the Human are quite cold. Confident that the Human will be slain by the hands of Asgore (if not earlier), Red shows extreme hesitance in befriending them on any level, even initially refusing to speak, as to "not lose someone else." In genocide route, you'll find out that she sort of likes humans but the rules "kill or be killed" means that she has to kill them (that's her secret no one else knows).
She doesn't member well, but she knows that her parents were killed in cold blood. She grabs a knife and chose to kill the human. After the war, W.D. Gaster took care for her and gave her power. His goal was to make a monster that is made for killing, but it failed. She was left in the cold at the waterfall (or other monsters call it, the Bloodfalls), stealing from people. Then, Undyne trained her, since she believes that Red has some fighting spirit in her.