This is a simple NO UMD FiX by Reborn, please NOTE once done the files consume 1.06GB:
1) Extract Syphon_Filter_Dark_Mirror_USA_READNFO_PSP-pSyPSP to a folder on your PC using iSOBuster or similar utility.
2) From your original PSP_GAME folder move ICON0.PNG, ICON1.PNG, PARAM.SFO, PIC1.PNG, and SND0.AT3 to the SYPHONFI folder from this pack.
3) Next, from your original PSP_GAME\USRDIR move all of the .PMF, .SUB, and .INI files (which will total 63 files, 385 MB (403,840,089 bytes)) over to the SYPHONFI\USRDIR folder from this pack.
4) Now, from your original PSP_GAME\USRDIR move the GAMEDATA and LOCAL_INI folders to the SYPHONFI\USRDIR folder from this pack.
5) Finally, from your original PSP_GAME\USRDIR\IRX folder move the following 9 files to the SYPHONFI\USRDIR\IRX folder (which already is included with some files in it) from this pack, ignore the rest:
6) Now follow the instructions as normal from the included NFO file:
Copy all folders contained in this release to the root of your memory stick.
Now boot using RunUMD.
NOTE: Although this is labeled a "NO UMD" release, that just means you don't need the actual SF: DM UMD in the drive to play the game, however, you will need a UMD in the drive to run it (any UMD game should work).