Can OS project published on Github be dual licensed for AGPL and EUPL 1.2? If so, what technically needs to be done for that?
So long as you are the sole copyright holder (or have the consent of all copyright holders), you can license code under any combination of licenses you like, including mutually incompatible ones (e.g. a closed source license and the GPL).
In order to do this, you should just follow whatever the instructions are in each license - e.g. adding the appropriate notice into every source file for the AGPL.
This is indeed one case where, as the original or sole copyright holder, dual licensing EUPL / AGPL makes sense, since the two licenses are both copyleft and similar on the key point of covering "network distribution" or SaaS. The EUPL has more compatibilities with other licenses and - because under EU law - has no "viral" effect in case of linking.