Well, here is my experience with this quest for anyone who is interested.
I first went after the Malboro NM. It apparently has a 100% drop rate on the item and a 21-24hr spawn time. I sat there overnight as my Summoner with time stamp to see if I could get the ToD. I read that it aggros at Lv75 so I left Carbuncle out the whole time.
Well, it did aggro while I was there AFK asleep and Carbuncle did kill it all on his own. I woke up pleasantly surprised to find the item for the quest in my inventory. Carbuncle essentially camped it for me. :D
Next I went after the Dodo. It took about an hour to get it to pop. I got claim and then it dropped. 1/1 on it. I did this as a Lv75 THF/RNG for widescan. I had a Thief's Knife too. With it's supposed 20something% drop rate and treasure hunter it should drop relatively fast.
Last I tried Nue. I HATE this ****. I went to camp him right after Dodo. I was there the whole night well over 5hrs before it popped. It ended up popping right as I was about to log off for the night. I got claim but no drop. I logged on the next day at the camp and it popped again in about 30mins. Still no drop. About an hour later I got it to pop again, killed it and got the drop. 1/3.
I used Thief again for Nue. No need for widescan since the spawn area is small. I had a Dancer sub for Animated Flourish(dancer version of provoke). It helps to have some sort of fast claiming for Nue because of the small area.
For a guy that HATES camping NMs in every sense of the word it wasn't too bad. Treasure Hunter helps a lot. If you don't have Thief leveled or have a buddie willing to camp it with you then you should really level a Thief sub.