Hello!
This achievement is super grindy and boring, but quite easy if you do it with some planning.
The achievement requires the following to to be completed:
Scholar of the Circle - Complete the Antiquities tutorial.
Master of the Eye - Reach the max rank of the Scrying Skill Line. (Lvl 10)
Master of the Spade - Reach the max rank of the Excavation Skill Line. (Lvl 10)
Meticulous Digger - Complete an excavation on Advanced Difficulty or higher while dealing zero damage to the antiquity.
To start being able to collect them you must travel to Solitude in Western Skyrim and speak to Verida Numita who will give you a short quest/tutorial. After this it's just grinding the levels by completing Scrys/Excavations. They level up at the same time if you excavate every completed Scry.
To level it up quickly I started in Galen (because its small) and repeatedly did the Zones green lead, then once levelled alternate the green and blue that's now available. Once you unlock Purple you can do 1 unique per zone, I went around the whole map clearing each of them until I was high enough to clear golds and only focused on Gold leads I had available until I reached level 10.
I would suggest building up a mass of these purple and gold leads and do runs clearing all available rather than going out of your way to find them. It takes some time so I just picked at it here and there when I had 5+ golds available while doing other content.
Good luck! =)