It's possible. It's quite difficult, but it's possible. You have to monitor your time quite a bit and get into as few random battles as humanly possible while being able to kill bosses at low levels, skipping through dialogue really fast and if you need to skipping FMVs.

I've gotten it. It's just a built in challenge. To get it because it's the most powerful weapon is rather pointless, because Steiner can already do 9999 damage with the Ragnarok, and Excalibur II bares no additional abilities. So it's just for bragging rights.