I want to reduce the opacity of multiple raster images and when I use the global opacity slider to do so, black borders appear between my images. I would want to eliminate these borders.
It looks like your rasters overlap slightly. When you make overlapping rasters transparent, the overlapped area will appear darker than the surrounding area. With an array of rasters, this creates the appearance of a dark border around the each raster.
Easy Solution - only works if the rasters are your base layer
You can achieve a similar visual effect without the borders by putting a transparent mask over the rasters instead of making the rasters transparent. This method only works if you were using the rasters as a base layer, because any layers under the raster will be completely hidden.
Create a new vector polygon layer and manually draw a polygon that covers all the rasters. Set the style to simple fill with no border, make the polygon fill white, and set transparency. 80% transparency for the mask layer creates a similar appearance to the raster layer transparency of 20%.
More complicated solution - if the rasters are not your base layer
If you need to overlay the transparent rasters on top of other data, you'll have to remove the overlap. You can do this manually with one of the GDAL Clip tools:
Since you have so many rasters, removing the overlap manually will take a long time. Using the batch processing mode of the GDAL clip tool will speed it up. Even faster ways may exist, such as automating the clipping with Python, or building a virtual raster.
Try boulding raster mosaic using Saga or GDAL: Combining multiple overlapping rasters.
You can solve overlaping issue and its much easier to manipulate with one catalog than with many rasters.