The marketing for Deathloop leading up to release heavily focused on the deadly relationship between Colt and Julianna, and finding out her true identity and reasons for hunting down Colt is a treat. Footage of the game showed the constant banter the two character would engage in throughout the game, and Arkane revealed that an AI or player-controlled Julianna could invade Colt's world and attempt to kill him. Despite all of these details, Arkane intentionally kept Julianna's connection to Colt a secret for players to discover whilst playing the game.
[Warning: Spoilers for Deathloop below.]
After waking up on the beach at the beginning of Deathloop, Colt is contacted by Julianna via his walkie-talkie, where she explains that she has been killing the man on repeat for a long time to protect the loop. Colt (and essentially the player) is confused by this confession, because it seems that his mission to kill all of the Visionaries would be beneficial to Julianna by allowing her freedom from the time loop. Colt also speculates about his connection to Julianna, offering up quips about how they must have dated before she started trying to kill him. Julianna never explicitly explains how she knows Colt, but a late-game twist reveals that Julianna is a lot closer to Colt than he imagines.
Colt learns from one of the game's many documents that his girlfriend, Lila Blake, had a child after he left for Operation Horizon, the original military mission to help understand the time anomaly that Blackreef Island was experiencing. He realizes that the child was Julianna, who shares the same last name as Lila. It's a reveal that adds a new level of drama to the proceedings, with Colt having either killed/been killed by his estranged daughter many times throughout the story.
Julianna's Motivations For Killing Colt
Julianna's reasoning for wanting to kill Colt in every time loop has many layers. Firstly, Julianna holds resentment towards Colt for seemingly abandoning her and her mother during Operation Horizon. It isn't technically Colt's fault, however, as he became trapped inside of Blackreef's time anomaly for 17 years and then was admitted into psychiatric care after breaking free of the loop for the first time. He never had any contact with Lila until he was recruited to be Head of Security for AEON, leaving Julianna without a father the entire time and eventually with no mother after Lila passed away.
Another reason that Julianna aims to kill Colt in every loop is to keep the Visionaries on Blackreef from being released back into the real world. Julianna believes that all of the Visionaries are extremely harmful to society, and sees it as her duty to keep them trapped inside the anomaly forever. Considering Colt is the only person that can break the loop by killing all of the Visionaries, it's only fitting that Julianna feels compelled to stop him, especially given that she's a Visionary herself.
During the sequence inside the Loop leading up to one of Deathloop's endings, Julianna also reveals that Colt started murdering her in an effort to free her from the loop after he started having second thoughts about the AEON Program. She got tired of constantly worrying about her father trying to kill her during each day, so she began hunting Colt down instead before he could get her. Learning about Julianna and her motivations is an enjoyable part of Deathloop's core experience, bringing interesting narrative reveals until the final moments of the game.