Dualsense works already quite good on Linux but need some improvement.

When I hit L2 it aims with the weapon and opens the menu at the same time. So I have to hold L2 and hit resume to be able to aim. Then I can aim but not shoot.

L1 should heal but does nothing. Instead the options button heals.

Turns out it is not a problem with the Dualsense. Even with the Dualshock 4 the button don't match correctly.

This problem caused by game not recognizing your device properly, I suppose. I`ve had same troubles with my DS 4, and this my solution:
1. start game from console, get id of your device ( 050000004c050000cc09000000810000 in my case)
2. find or write by yourself right mapping ( For example, I found right one for me here : )
3. open gamecontollerdb.txt in /path_to_your_game/Hyper Light Drifter/game/assets/ and add entry with data from 2

I hope it will work for you too

op, mark the above comment as the solution; it worked well for me.