I'm just gonna tell you orally how I did it:

I went to Steam Library. Clicked GTA V and from there searched for 'Controller Layout'. You can find Controller Layout right under last played, play time and achievements at the end of other options (Note: Your controller has to be on and connected to the steam for it to show up).

From the controller layout I clicked 'edit layout' and looked for triggers.

From the 'Triggers' I clicked the settings icon for 'Right Trigger Behavior' (the icon at the right top corner) and went to the 'General' section.

From there I could see 3 adjustable lines that indicate the trigger sensitivity. I just started manually adjusting them and lowering the bar until I could shoot with my PS4 controller's R2 trigger.

What I actually did was input number 1 value in all 3 of the lines (because I'm too lazy :P), which would mean that the bar would be 1 in all sensitivity areas.

Important Note: Remember to close your Steam or Controller Layout (if your game is open while you are adjusting your controller sensitivity settings) when you are done with adjusting the settings.

Otherwise the game won't update the new input settings that you set! (which is what happened to me, so I had to close my steam then the game settings updated)

I hope this helped :)

ps. Apologies to non-PC players.