Disclaimer: I did not create this or discover the command that it uses. It seems it was originally discovered by a modder known as "tchi6". I'm not posting this here to claim credit for it, I just don't see it properly listed anywhere so I figured I'd do it myself.

Disclaimer 2: This may not work if you don't own the Season Pass. In that case, you should be able to use the console command approach mentioned at the bottom of this description.

Disclaimer 3: I have personally only tested this with the Steam version, though I would expect it to work with any version.

This is a fairly simple config file edit that allows you to attach the camera directly to Batman's (or any playable character's) skull during gameplay. Super janky and sometimes outright unusable (the game simply was not designed for this), but can be pretty amusing.

To install, extract the files and place them into the game folder (i.e. "Steam\steamapps\common\Batman Arkham Knight\", or wherever you have it installed).
Press 'o' to enable first person.
Press 'i' to set the camera back to normal.

You can rebind these by editing the config file in "DLC\356474\Content\BmGame\Config\BmInput.ini" after installing. To uninstall, simply delete that file.

Alternatively, if you instead want to do this with the Definitive Console Commands mod or some other method, these are the actual commands used.
Set BmGame.R3rdPersonCamera DoAdamsCrazyCam 1
Set BmGame.R3rdPersonCamera DoAdamsCrazyCam 0