I wish I had counted the number of times I did certain quests to get enough fame for this, but I don't have an exact count...so here's my estimate. I went through 10 Goblin goods for the Getting Lucky quest, meaning I did that 10 times. I did the Woozyshroom Chocobo quest once and got the atma. I did The Egg Enthusiast about an equal number of times as the Goblin one. I did the Wyvern Rare Item to Corneilia I think 3 times.
THEN, because I forgot and never saw any Shock Spikes on the NM, I never used the Elixer, and didn't get credit for the quest. So I had to do it again...and I died, so I'm going back for round 3. :( Died on attempt 3 also. Don't know how #1 felt sooo easy and 2 and 3 just beat me. It's Thundersday for attempt 3 and I still had resists on VF stun, even though I had no resists on the first attempt. I hate random...
04/02/2013: Just did the quests to trigger this quest. Decided to note down how many of the Wivre Egg (by Ronpi-Monpi) it took in order to reach level 3 Reputation. If I'm not mistaken, I hadn't done other quests in this Abyssea zone, and it amounted to 9 Quests required to reach level 2 and 10 quests required to reach level 3.
After the 10th quest in level 2 fame, spoke to Brugaire and he gave me the Prismatic Elixir. -Tarusofo on Ragnarok server.