This page in our guide to Judgment has the walkthrough of the prologue.
After the cut-scenes, you will take control of the main character - Takayuki Yagami. Your first task is to defeat a group of enemies. The game will teach you the combat secrets by showing a brief tutorial on how to fight. Deal with the enemies.
Then, go to the red marker on the map. Your goal is to find the character from the drawing. Look at the picture and select the character presented in the screenshot to continue the plot.
Now it is time to tail the target. Keep a safe distance and tail the character without filling up the Caution Gauge visible at the top of the screen. Follow the man and hide behind the objects (they have a blue field in front of them) to avoid detection. Follow the target slowly. When he turns, hide behind the nearest cover. Soon, the tailing sequence will end.
Time for a Search Mission - you have to find your drone. The object is in the sky - find it and press X to continue.
The wanted man escaped - time for a chase. Yagami starts to run automatically - your task is to avoid obstacles. Press the appropriate buttons to make your hero jump over them, or make a quick dodge. When you get closer to the target, press O to capture the man.
Time for a 1vs1 fight. The game will teach you how to change the fighting stances - Way of the Tiger is perfect when you fight single enemies. Defeat your target using different combos. When the enemy falls down, you will watch several cut-scenes. This marks the end of Judgment's prologue.