I tried to make EDS mapping of a medium Mn steel in the sem but I observed that there is like an interaction between beam and sample so that the image was continuosly moving and it affected the maps.
Don't use adhesive tape, sometimes it has poor conductivity or can be mechanically unstable. Just glue your sample to the stub with carbon or silver conductive paint (e.g. Ted Pella DAG-T-502).
If the movements are jagged back and forth, the problem is charging. Make sure your sample is well grounded on the specimen stub; if you use cnductive carbon tape thta is not working well, you can add another connection to eth stub by conductive carbon or silver paste.
If the movement is gradually over time and always in one main direction, your problem is thermal drift. Use the built-in drift correction to compensate it. If that does not work, use electron beam shift manually every few minutes to ensure a feature you can clearly discern will stay in place.