One simple solution would be to delete the file, then fill the memory with any other data so the space previously owned by the deleted file is sure to get overwritten.
Once the memory is filled up, the file(s) used for the filling can be removed, releasing the space again - only now recovery attempts will find only the filler file, not the original deleted file.
Note that this is intended only for combatting simple home recovery tools like
testdisk. There may in theory still be ways to recover at least parts, or even the entire original file - however they would require some sophisticated high-end analysis methods. One example of such a method would be to analyze if some of the data is preserved because of flash wear leveling. However this isn't easily done, and AFAIK would require connecting the memory card to a custom reader device of some sort, and might even require taking the memory device apart.