From quite far from Arkham, New England: Spain.
Don't you think that combat Cthulhu isn't so hard as this Ancient One deserves?
I mean, it doesn't matter how many "points" of stamina or sanity, It atacks the maximun level; so, if you have an standard 5-5 investigator, 4-4 resolving the permanent effect of Cthulhu, you have 6 times receiving Cthulhu's atacks before you die… I find it a bit dissappointing, and you?
One doubt: An investigator can try to complete the task any time he/she wants, but I assume that if you can complete one time those dice are fixed each one in the part of the task, I mean: you haven't all the dice to try to complete the task again, have you? (is it my English enough clear?)
Lovecraft's lovers: a hug from this side of the ocean
Welcome from England, Mad is in Germany if I remember correctly
First, let's address your question concerning how many times you can complete the task during your turn.
If you roll the 6 green dice and manage to roll Law, Peril and Terror on three of them, then those three dice are set aside (i.e.placed on the task on the AO card). You now have three green dice left which you can roll again, so in theory it is possible to succeed twice during your turn (as a matter of interest, you only have a 1 in 36 chance of rolling Law, Peril and Terror with three green dice).
Even if you add the Yellow and Red dice to your dice pool, you can never manage to succeed more than twice during one turn (because to succeed a third time would require a total of 9 dice). Of course it will be easier to succeed once or twice using 8 dice than just using 6 dice but the point is that each time you manage to roll the requirement (i.e. Law, Peril and Terror), then those dice are set aside (just as when you attempt a normal task on an Adventure card).
Cthulhu is easy but only if you have Items, Spells and / or Clues (plus any Special Abilities the Investigator may have)..
If you use just the 6 green dice, then you have a 43.2% of rolling the required Law, Peril and Terror during your turn. You do have a chance of succeeding twice but as mentioned, you would be rather lucky if you did. Given that you have a 43.2% of succeeding, then on average you will take something like 25 to 26 turns to succeed 11 times (11 because you are required to remove 11 Doom tokens to defeat Cthulhu).
Trouble is, Cthulhu adds a Doom token every 4 turns (i.e. every time he attacks a Doom token is added to the Doom track). So during those 25 turns it takes to remove the original 11 Doom tokens, Cthulhu would have added a further 6 Doom tokens! To remove these additional 6 Doom tokens will take a further 14 or so turns! This means we are already at 40 turns and we have established that at best you only have 28 turns maximum to defeat Cthulhu (if you are wondering why 28 turns max, then please have a read of my post on BGG, Unfair devouring against Cthulhu?).
So in summary, if you are only using the 6 green dice, there is little hope in defeating Cthulhu. If you can add an Item or two each turn then it becomes much easier.
Of course there are only 18 Item cards that allow you to add the Yellow and / or Red dice but given that the investigators have a fair number of these along with Clue tokens and Spells, it does become easier to defeat Cthulhu. The more you have the easier it becomes. Going into Final Battle with only a few of these will most likely end in defeat.