Edit: I just paired my Dualshock 4v2 with my U9-H. I didn't experience any noticeable lag, but the U9-H has no .kl file for the Dualshock 4, so mapping is all wrong.
DPad: works as expected
Cross: BUTTON_B
Circle: BUTTON_C
Triangle: BUTTON_X
Square: BUTTON_A
Share: BUTTON_L2
Options: BUTTON_R2
Touchpad button: BUTTON_THUMBL
L1: BUTTON_Y
L2: BUTTON_L1
L3: BUTTON_SELECT
Left stick: AXIS X, AXIS Y
R1: BUTTON_Z
R2: BUTTON_R1
R3: BUTTON_START
Right stick: AXIS RX, AXIS RX
This doesn't matter if you can remap the buttons within the game (Dead Trigger 2), but the weird mapping can be fixed if your willing to root and install a .kl file.
Original Post:
Native support for the Sony Dualshock 4 is only on Sony Android devices or Android 10 devices. If you must use a Dualshock 4, I would get the 8bitdo Bluetooth adapter for the PlayStation Classic. There are other options that involve rooting and other stuff, but I think the 8bitdo hardware solution is best.