If the file is on a sdcard then you could insert the sdcard into your notebook card reader and use
sdelete or whatever you usually use on your desktop for secure file deletion.
If the file is in the internal memory then probably the only reliable way to completely delete any trace of it (and everything else on the phone) would be to enable full phone encryption in Settings > Security, wait until everything is encrypted (about one hour), and then do a factory reset.
There are also apps in the play store that allegedly can wipe the free space with DoD level algorithms, but I have no idea how good they are or how they work.
And btw, keep in mind that flash memory has a limited number of read-write cycles, so running those apps too often can potentially reduce the memory chip lifetime.