It seems that ai to dst conversion is typically sought by users that are trying to convert their logos and designs from Adobe Illustrator (.ai) to an embroidery design (.dst) file for Tajima machines.
Most embroidery designs tool won't open AI graphics, but should support import of SVG graphics. So if you have access to Illustrator, try to export your graphics to SVG format, or use any of the available ai to svg converters.
You can also find several commercial plugins for Illustrator and CorelDraw that allow users to both import, export as well as edit embroideries in DST format. The most popular add-ons including Illustrator Extreme and Embroidery i2 for Adobe Illustrator.