You have to ask the sneevil dump site quest from the treasure hunter. She is standing beside a HUGE gold statue. To find it, go to Falconreach, go to the right until you find the entrance to Surewould forest, but take the lowest path (the one below). If you have trouble, talk to Willy in Falconreach.
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You must have completed the previous quest, Jars of Slime, to unlock Sneevil Boxes.
To find the healing jar this is what you need to do... 1. Accept the quest from Dew Drop the Forest guardian. 2. From there go to the left until you see a clearing with 3 Sneevil's in it, and a purple tree-like thing in the distance. 3. Of the 3 Sneevil's in the clearing the one in the middle has the Healing Jar 4. Defeat the Sneevil and you will be rewarded with the Healing Jar. *NOTE* This worked for me however it may not work for you. It could be different for everyone, I do not know.
It is now rare but you could have gotten it by completing the Undead Defender Quest 'Pactagonal Armet' or the Sneevil War Quest 'Pactagonal Armet'.
The Zard War (part of Resident Sneevil) can only be currently accessed in the run up to Halloween. (Until its added to the war memorial)
It is actually not as hard as you would think. Refer to: http://forums.ngemu.com/pcsx2-forum/84994-guide-dump-bios-through-usb.html for directions to dump your PS2 bios onto a USB Flashdrive. And on a side note, when you dump your bios using a custom code (as explained in the above link) you are actually copying your bios, so it does not render your PS2 useless.