Quantum Break Walkthrough Guide: Act 1 - Part 3 - Library Chase
At the End of Act 1- Part 2, you get inside the building you will see the echo indicator blinking so activate it to investigate the area to see what happened. As you head up and open the Door you see you are freezing the time and running at light speed, you will soon take cover and finish off the remaining guards. This new ability is called the Time Dodge where you skip the area fast to avoid the Bullets.
Try to use this new Ability the right way and avoid taking all the bullets. Take the guards down and then head inside the room. There are a couple of enemies waiting for you so take them down one by one and then head downstairs to take up the next bunch and as you head outside the building you see the Guards are taking Will inside the Library so you need to find another way to trespass in.
Get into the Library
Head left to see the alternative entry to the Library you need to jump on the Obstacles to Climb up and get to the next area. Once you get inside you will have to look from the Obstacle Right with Red Container on it, now as jump you see the Blue Lift which goes down as you jump on it so you need to stop the time as well as be fast enough to jump on the other side then take the ladder to climb up and finally inside the Library Window.
It's Dark inside so make use of your Time Vision to locate the clues and get to the lower area to kill the Guards. You hear them saying that they have planned to blow up the Library so you need to hurry and find William asap. Locate Will and as you enter the Door you will learn a new ability of Time Shield where you can dodge the bullets with the Shield.
Your Primary goal is to clear the area of enemies to take it your way by making use of the best abilities you like and finally meet Will to help him get out. But wait few more of the Monarch Guards have Ambushed the Library and wants you and your brother down so let's take them first.
Survive the Ambush and Escape with Will
As you said before you can take them down with your own skills and the abilities you select just make sure you don't die. Once you have cleared the Guards go and talk to Will as he is the one who knows Beth Wilder and needs his Briefcase from his car as well.
As you are about to escape the cutscene will start where you see two the Guards with their boss who is Paul himself. He Kills you brother William by collapsing the Library and at the end, Paul's men Liam Burke hits on your head and thus Ending the part one of the Game. This is the End of Act 1, continue to check the Quantum Break Act 2 Walkthrough or check the Quantum Break Wiki Guide to know more about the game.