Upon beginning the Halo 4 campaign Chief awakes and exits the cryo tube. Walk forward and there is a stair case on the left hand side that takes you beneath the walkway you start on.
Under here behind you when you go down stairs is a terminal that you can press
on to access Master Chief's records. You will need to press
a few times to continue when prompted. (Im not sure you need to do this as my achievement pop was broken at the time)
Here's a video.