In order to complete the Case Files in Battlefield Hardline, you have to find all the evidence which is required. By locating the evidence you will also unlock the following four achievements or trophies.
Keep Digging, Detective which is a bronze trophy and gives 20 gamerscore points, True Detective and Bring 'em to Justice, a silver trophies which gives 25 gamerscore points each and World's Greatest Detective which happens to be a gold trophy giving 50 gamerscore points.
You search for the collectibles will be easier with the help of a scanner as it emits a specific sound whenever you are near a collectable. The scanner will also highlight evidence in the game world when aiming at it and can be used to tag suspects with warrants.
Scanner also shows the count of collectibles available in the area that you are in and also you will see an arrow in the top left corner that shows the distance to the next evidence and points you to it.
Even if you lose a life while collecting the evidence you don't have to start all over again. New weapons and equipment will be unlocked as soon as you collect the required evidence.
All progress is saved instantly and you can quit out to the main menu without having to reach the next checkpoint. To arrest suspects with warrants you must use non-lethal means (taser or handcuffs).
Watch the following video from PowerPyx for Battlefield Hardline Episode 1 Collectibles: