I have added the original PS2 version on emulator as a New Game category similar to the console: https://www.speedrun.com/dmc3se?h=dante-s-awakening-emu-Normal&x=7kjwmezd-6njzk6l4.4lxrx4l2. The rules are as follows:

Speedrun begins at the last selection in the main menu for NG and ends at final hit of Vergil 3; NG is restricted to non-super Dante costumes only. All runs require permanent video. The only emulator allowed is PCSX2. The game must be played in the original 4:3 aspect ratio. The emulator's Hardcore Mode (System -> Settings -> Achievements -> Hardcore Mode) must be enabled and shown at the start of the run by attempting to use save states, cheats or slowdown functions. The following System settings must be displayed: System -> Settings -> Graphics -> OSD -> Show OSD Messages, Show FPS, Show Frame Times, Show Speed Percentages, Show Resolution, Show Indicators, Show Inputs.

You need to make an account on https://retroachievements.org/ and log in in the emulator to enable Hardcore Mode. You need to restart the emulator a couple times to enable the log-in function and Hardcore Mode.