I may have been Lv155 at the time, but I was only on Floor 77. I did a lot without advancing the story real fast, not wanting to miss anything.
The secret to leveling these weapon mastery points fast is to almost do nothing, really. Just have patience. *Auto-attacks are the key*. Find a durable boss that you can handle, but can also take lots of hits from you. Use all the skills I used, which increase attack speed, shorten attack delay, and increase the chance of double auto-attacks. You saw my mastery in daggers go from 799 to 802 relatively fast, and that enemy was a lower level than me.
It also helps to not have a partner with you, since they will kill your valuable targets. The area I'm in is a temple known as... Garden Paradise - South, I think. It's accessed from the Garden Paradise - North teleporter. Just travel along the path until you see the 3 walking flower monsters, and make a right at them, into that temple. There's like 2 NMs in there. One's a tree and the other's a reaper at Lv136.
I've long since gotten full mastery in all weapons, even long before others at higher levels than I, who still don't have full mastery. We just all improved in different areas. But if you wanna level up your mastery, you need dedication, and some down time lol.
Also if the screen looks like it's shaking, it's because I'm tapping the analog stick into the enemy, because moving slightly and stopping (after Kirito's done an auto attack) will make him do it again, faster than just staying still.