Hello PS4 controller user,
This is a simple guide to get your PS4 buttons mapped to PSU's controls correctly. It's much simpler than the Xbox controllers.
First, in your PSU Clementine folder, open the "online.exe" executable and click on "Options". (You can also open options from the launcher)
Open "Gamepad Settings," and then map the following controls to your buttons.
(IF YOUR OPTIONS SHOW AS ??? THEN DO THE FOLLOWING): Press Windows Key + R to open Run. Enter %localappdata% and hit Enter. Go to the SEGA folder, then the PHANTASY STAR UNIVERSE Illuminus folder. Open the Psuilluminus.ini file inside with text editor, and change the line LANG=J to LANG=AE. Retain any spacing the file already had. Save the file and open "online.exe" again (or reboot your launcher) and go to Options to see the corrected text.
Enter, talk, search, pick up item - Button 2 (X)
Cancel, bring up action palette - Button 3 (Circle)
Normal attack, bullet, TECHNIC - Button 1 (Square)
Striking weapon skill, TECHNIC - Button 4 (Triangle)
Lock-on camera, next page - Button 5 (Left Bumper)
Switch weapon, next page - Button 6 (Right Bumper)
Page left - Button 7 (Left Trigger)
Page right, Chat Log - Button 8 (Right Trigger)
First person camera ON/OFF - Button 12 (Right Analog Stick Click)
Main menu display ON/OFF, skip movie - Button 10 (Start Button)
Change Character Info Display - Button 11 (Left Analog Stick Click)
UP, RIGHT, DOWN, LEFT Arrow Key - None
Camera left/right - Z axis
Camera up/down - Z axis rotation
And with that, you should have a fully functioning PS4 controller WITH TRIGGERS and no 3rd party program required. To type in game, simply press the Space Bar.
NOTE: This guide is purely to replicate the controls that the Xbox 360 used on the Official PSU server.