The following lists should work for any recent release of the named distros and derivatives. However, for some modules, some distros might ship versions
that are too old. These should be installed through pip until the distro adds/updates the package.
(This is what I use personally and it works great - it's basically just a script which installs dependencies, clones the source from the official repo and puts it in the right place.)
Even if not installing from the AUR, the above link has a full and up-to-date list of the required package dependencies.
Note that you can use PyQt5 instead of PySide2 (however PySide2 is recommended). If you choose to use PyQt5, you don't need PySide2 or shiboken2 but have to install python-pyqt5 and python-sip-pyqt5.
You also need python3-qtpy, but the version shipped by these distros (as of this writing) is too old. At least version 1.8 is required. Until the distros catch up, it is recommended that you install
this module with pip instead of the package manager.
You might need to install the shiboken2 module from pip since it looks like it is not currently packaged.
Instead of PySide2 (the python3-pyside2.* packages above and shiboken2), you can also use PyQt5 (python3-pyqt5, python3-sip), though PySide2 is recommended.