I have tried to use DualShock 4 with BloodGDX and here is my experience that could be useful for somebody with the same controller. There is no native support for DualShock in BloodGDX 0.794 (it is detected but does not work correctly), but there are DualShock to Xbox controller wrappers available that can help. I choose DS4Window and it works well with few tweaks. In DS4Windows settings should be enabled "Hide DS4 Controller" or the game detects DualShock as two controllers. Also there is need to increase L2 and R2 triggers sensitivity, without it pressing of these buttons is not always detected (1.5 value worked fine for me and there is DS4Windows 1.4.53 build that can increase it even more). Otherwise it works well - I used default bindings for all buttons in DS4Windows and configured gamepad as I liked in Blood GDX settings where it was detected as Xbox 360 for Windows.
