You go to the library if you pick the option "On second thought..." when Kirishima is debating whether to ask Bakugou for help or not.
i picked that option but i didnt go to the library. im stuck on the go to sleep achivement too
Ok i figured it out. i got the sleep achievment. you need to get the bad ending and then immediatly start a new game and then pick the on second thought. then it sends you to the library