The Chaos Drill obtained from Item Girl at Gate of Black Swamp is the best in-game drill to use in this case.
Its lifespan is 600 with a max depth of 120m.
The room to drill for the Earthen Fate Necklace is 120m max - perfect!
Any other higher level drills that cost 100k+ may have higher depths (which you don't need) but the lifespan is significantly shorter. So you end up wasting your money!
You can also use the Poppuri Drill(s) if you have them.
Those work wonderfully well, too.
You can also spend points to opt for the MyShop drills but why would you do that?
Basically, go for the Chaos Drill if you want a good in-game drill.
Edit 1: You may want to put on some DA equips so obtain the stat of DA 90 in total. This is the supposed amount of DA you need to help you identify if there are items to drill in that spot.
Edit 2: Looked around wiki & found that the max depth in the Room of Light is 120m.
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Last edited by Boba; 07-29-2012 at 11:30 AM.