Yellowgremlin will show you the name of the leve if you search for it and then change the language to Japanese. I've mostly been grouping with JPs since English speakers on Figaro don't seem to group outside of their linkshells. Here's some of the names used for Broken Water and Halatali leves here, they generally refer to the name of the mob you're killing.
コカトリスたまご or コカ - All Cracked Up (Cockatrice)
デビレットの捜索 - A Devilet's Best Friend
アルドゴート - A Terrible Thirst (Aldgoat)
ペイスト - Dunesfolk for Dinner (Peiste - this might refer to the mole leve too)
モール or モル - The mole leves. Could be any one of a few at Camp Broken Water
ナット - Netting the Gnats
ゾンビー - Restless Be The Damned (Zombie)
ペイスト - Peiste again, I don't remember the leve names but there are a couple ones.
ヂッガ - Preventing the Plague (Djigga)
風使いの捕殺 - Secrets of the Sultanate. I saw someone in my party call this just 風使い. They'll probably also understand if you use ウィンドエレメンタル (Wind Elemental) since this is the only leve at Halatali with them.
アサシン - Juggling Knives (Assassin)
If I remember any more I'll post them here - this is just what I have saved in my google translate window.
Edited, Jan 24th 2011 5:47am by Wbrannigan
Edited, Jan 24th 2011 5:48am by Wbrannigan