you need to collect all the clues to avoid doctor rose death, a commentor posted how before, i'll past them here.
- look out the window on the first night to witness kidnapping
- go for the run before you sleep (you can choose either park or pier, if you choose pier choose the longer route) and linger at the scene
- show some kindness! (go to the man kneeling)
- while on asriel play date with sweets choose swan park to witness more kidnappings
- there will be two times where player can choose what to do. first time being (hobby)(daisy)(lunch) and second being (rest)(daisy)(pillow). for the first choice choose (daisy)(lunch), the second choose (rest)(pillow)
- after choosing (rest) make sure to investigate the apartment and press the dude for information regarding his son, do not let the subject go. select “What if they’re all connected.” when it pops up
- at the black swan after papyrus asks you to show up, don’t leave on the first choice but leave with chara and asriel after they ask you
- at some point there will be an option to check out the apartment before or after the run, choose before
- also when you interact with the neighbors son if you want to learn about the deathless beast choose (compliment rolex)(he adores you)(looks forward to your visits)
hope this helps!