I don't think it's possible right now. With a Gigantix's forced despawn timer and the game reducing your damage to nothing if you attack anything that's too high level, there's no way you'll have the DPS to kill this thing before it despawns.
The only way you'd have a shot to kill this thing is if it doesn't have that level dependent damage reduction.
Then if it doesn't have enough DEF to reduce your damage to nothing again, then you might have an actual shot to kill it.
Even assuming it's possible for you to achieve high enough damage numbers to kill this thing before it despawns, you'll have to do it without getting hit a single time because this thing will surely OHKO you.
It's a lot of IFs, but go give it a shot if you want. Do come back and let us know how you did though. I am wondering if Sega has the ability to turn of that level based damage restriction for specific mobs.
Why did Sega choose to add a boss that's level 64 when game restrictions arbitrarily block us from ever being able to kill it? I don't know.
The entire zone of Halpha Lake is an anomaly. At launch the zone had nothing in it. No monsters. No gathering nodes. Nothing. This boss at least fits the zone, in the sense that it's another anomaly.