katana with water/ice element

I am trying to use/familiarise katanas for a change(been using sns since mh and mhf) and so far trying missions with a katana with thunder element. Is there a katana with water/ice element. I recall there is a possible path after GS halberd->judgment->katana??

There is only Frost Reaper (and the level above), that is a path of the Hallberd, but unfortunatelly for you (I think) it's only available online, so you'll have to play online (like me) or using cheats to get the hard quests, to get the item needed to upgrade it

i just got it last night, after the halberd and its improvement there is an option for a large sword that looks like slice of honey dew on a stake (that requires 3 funny rare-5 bugs only found at TOWER area) then you have the 3 options

1)improvement of slice of honey dew on a stake
2)the reaper/scythe with fire element
3)the reaper/scythe with ice/water? element

fire reaper was available while ice/water? reaper needs monoblos hide and bug juice/monster fluid, everything is offline.

maybe the upgrade after requires online items?

finally got the ice element scythe but the sharpness just a hint of green aargh, how to improve the sharpness? according to http://mmpotato.hp.infoseek.co.jp/codes/MH2, it can be upgraded to Froth tree per but what is

Angular ×3 of silver
The snow Jishi it is sharp fang ×2
[monoburosuhato] ×1

First: fang from silver Rathalos I think
Second: fang of Dodobrango
third: I have to search, I'll reply soon (hope)

silver rathalos? that is online material right, i guess i have to make do with little green sharpness and supplies of whetstones.

yep.... there absolutly NO weapon with blue/white sharpness offline except garuruga that you can only fight offlien by having MHF on psp