Glue/adhesive/epoxy for soldering a mems microphone
The microphone works, but it is not held in place since the solder connection with the metal does not form a strong bond. 


If 4 soldering points cannot hold practically weightless component in place then you did not solder it properly.


  solder the microphone and then make sure that the microphone connectors are touching the metals, and apply super glue to keep it in place. but this is not a clean solution.


IMHO it is actually the best solution. I don't understand why you think it is "not clean".

Here is what I would do (basically a variant of @laptop2d suggestion in comments):


clean MEMS contacts thoroughly. Put a drop of solder paste on each pad and heat it up to form round blobs. You can also make a simple solder mask by punching 4 holes in suitable material, but it is not required. I recommend watching some "BGA reballing" videos for example.
clean PCB contacts thoroughly, use some no-clean flux, cover them with solder, then remove as much solder as you can with a wick.
add solder paste to PCB contacts. Here that mask will come handy again. Position MEMS in place so that the balls you made earlier sink into paste blobs. Heat the whole thing up to solder it in place.
Make sure MEMS works, then put a drop of thick CA glue at the MEMS edge. It should seep under the part on its own.