It is impossible to make an embroidery file like TAJIMA DST from a bitmap source like GIF with just some common graphics editor. This is because embroidery files are special vector based images with instructions for the stitching machine.
However, an experienced graphics designer might be able to create embroidery design from some image, which might essentially achieve gif to dst conversion. This is done with usually expensive digitizer software. Some embroidery software can also possess basic digitizing function that can convert raster image to embroidery, but that's usually far from perfect.Open GIF file Open DST file
An embroidery designs manager
A set of applications used by professional graphic designers
An embroidery digitizer