I haven't done anything like this before... buut (pretend the A is 4x4 instead of 2x2)
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using buckets (O = obsidian wall) Go inner->outer to avoid cave collapses. Once you dig out the inner obsidian walls, the adamantine can be mined without fear (of magma). to keep going, dig out the obsidian walls and channel the floors further.
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dig out the inner 2 rings of obsidian (ADD A SUPPORT TO THE OUTER RING FIRST), channel the middle ring into the magma again (o = open space over magma, f = obsidian floor)
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mine the Adamantine, pour water over the open spaces creating a smaller ring of obsidian 1 level below, again starting with the inner ring first. Remember the inner ring is support for the outer ring, but once the outer ring is cast you need to add a support to it before channeling the inner ring.
A 3-thick border of obsidian will give you access to 2 levels of adamantine, and each level down takes increasingly more work. On the upside, you can plan for 2 levels and use what you've done to extend it to 3 without wasting much of your previous work.