Try Clip tool in ArcToolbox.
1. Add all raster files you want to clip to ArcMap (actually this is optional only. You can browse to your raster data later if you don't add them to ArcMap)
2. Add your clip feature to ArcMap (most likely it's a polygone shapefile). This is also optional only.
3. Now open ArcToolbox.
4. Go to Data Management Tools --> Raster --> Raster Processing
5. Double click on Clip (this will open the toolbox).
6. If you want to do batch processing, right-click instead of double click and choose Batch...
7. It's better if you try a single processing first to see if it works for you.
8. The toolbox is self-explaining, so I won't give any more explanation.
9. Don't forget to tick the Use Input Features for Clipping Geometry (optional). This checkbox will tell the toolbox to ignor the X,Y max, min values given on top.
10. Name your raster without an extension if you want your result as a GRID format.
11. Click OK and that's it.
If it works for a single processing, there's no reason it won't work in batch processing.
Tell us if it works for you. It always works for me so far.
Good luck