Install HENKaku: https://www.youtube.com/watch?v=bQEPnRMP5cg
Install VitaShell: https://www.youtube.com/watch?v=q8W5jnv17xk
Step1: Download the file above and use VitaShell to establish a USB connection to your PC with your PS Vita.
Step 2: Navigate the the "ux0:/" root and copy the "pcsx_rearmed.vpk" to the root of your memory stick.
Step 3: Navigate to the "ux0:/data" directory and create a folder called "retroarch" the inside the "ux0:/data/retroarch" folder create a folder named "downloads" This is where your PSX.BIN files will go.
NOTE: You dont have to make these folder because the installation of RetroArch will create them for you.
Step 4: Once you've made the directory and placed your PSX ROM in the ux0:/data/retroarch/downloads folder on the PS Vita, exit USB in VitaShell and navigate the the ux0:/ root and locate the pcsx_rearmed.vpk and press X to install. Then hit X to confirm.
Step 5: Once the emulator VPK has installed, exit VitaShell and locate the RetroArch bubble and open it. Once open, navigate to "Load Content" and hit O, within the emulator O = confirm and X=Back.
Step 6: After selecting load content navigate to ux0:/data/retroarch/downloads and selecrt your PSX.BIN to load and hit O and the ROM will load.
NOTE: No bios means it might be buggy, all saving works tho just try to save as much as possible.