After beating Ys II for the first time, there are mandatory extra cutscenes that players will see during future playthroughs. As these are unskippable, they add roughly 1:40 to a run done on what is essentially a "New Game+" mode. So, naturally, you'll probably want to revert to "1st playthrough" settings for a free 1:40 time save, as the cutscenes in question aren't present during your first time through the game.
Depending on the version you're playing, how to do this varies. If you're not seeing the scene with the Goddesses and Lance's elder after starting a new game, then you've successfully reverted the game to its "first playthrough" state!
If the steps listed below are incorrect, or if you know a simpler way of doing things, please let me know!
(Thank you to Freedom_Pulse and XSeed's programmer Sara for helping me to figure some of this stuff out!)
Chronicles+ (Steam)
For the PC versions of Chronicles and Chronicles+, you'll need to delete a file called "autosave.sav". Please note that this file corresponds to both Ys I & II. Primarily, it contains your Time Attack times for both games, the clear data for Ys II, as well as what character mascots you've obtained in Ys II. In addition, this file keeps track of any in-game personal preferences (soundtrack choice, whether EXP is displayed as the total amount obtained or to the next level, etc.), so that stuff may need to be re-configured depending on your tastes. If there's anything from this file you'd like to keep around, then keep a backup of it handy.
If you're playing on the Steam version of the game, you'll first want to disable Steam cloud synchronization for not only Ys 2, but Ys 1 as well. To do this, right-click the games in the Steam library, go to "Properties", and on the "Updates" tab, un-check the box that says "Enable Steam Cloud synchronization". The reason you do this for both games is because the "autosave.sav" file shares data from both games, so even though what we're doing here only pertains to Ys 2, Steam can still salvage an updated copy of the "autosave.sav" file from Ys 1 if Steam cloud syncing isn't disabled for both games (Steam will automatically update this file every time you load up either one of the games).
After that, you'll want to find out where the "autosave.sav" file is located. If you're not sure, check the location listed in the game's configuration program:
Please note that there are actually two locations Steam saves the files: the location given in the configuration program, and in Steam's directory. The path to the Steam saves is in the "userdata" folder, under the game's ID, #223810. To clarify, these are the two paths to the files on my PC (this may vary between users):
C:\Users\jeff\Saved Games\FALCOM\ys12c D:\Steam\userdata\64952620\223810\remote
Once you've located the "autosave.sav" file, it needs to be deleted from both locations. If it isn't, Steam will simply grab the file from the other location to use as a backup.
Chronicles+ (GOG)
Currently, the GOG version doesn't support cloud syncing, although it's likely that it will in the future. For now, all you need to do is locate the "autosave.sav" file (check the game's config program if you're not sure where it's located) and delete it. For reference, this is where it's located on my PC:
C:\Users\jeff\Saved Games\FALCOM\ys12c
In the likely event that GOG does support cloud syncing in the future, what will likely need to be done is something similar to the steps for the Steam version. In GOG Galaxy, if you click the "More" button for the game (right next to "Play"), then go to "Settings", there is a "Cloud Saves" section for games that support it. If these games ever do support such a feature, then you'll likely need to un-check the box that says "Sync local saves with GOG Galaxy Cloud" (as with Steam, there's a good chance this will need to be done for both games, as the file in question has data from both games).
From there, you'll then likely need to locate and delete "autosave.sav" from both locations: the one listed in the game's config program, and on GOG's end. To clarify, these would likely be the two paths to the files on my PC (this may vary between users):
C:\Users\jeff\Saved Games\FALCOM\ys12c C:\Users\jeff\AppData\Local\GOG.com\Galaxy\Applications[App#Unknown]\Storage\Shared\Files
Chronicles (PC)
All you need to do is locate the "autosave.sav" file and delete it. I don't think the config program tells you where it's located in this version, but for reference, here's where it's located on my PC:
C:\Users\jeff\Saved Games\FALCOM\YsC
Chronicles (PSP)
The easiest thing to do would be to play without a memory card, or on a separate memory card that hasn't beaten the game yet. Failing that, I believe the system data file for Ys I & II Chronicles contains the relevant data, so deleting that should do the trick (it should be the file at the very top of the game's "Erase" menu).
Eternal and Complete (PC)
Unfortunately, I think the only way to get "1st playthrough" settings again for either of these versions is to un-install and then re-install the game. I believe this wipes your individual saves as well (something you shouldn't need to worry about with other versions), so be sure to back those up before proceeding to un-install the game.
