When in G.A.R.M., go to the drill control room overlooking G.A.R.M.'s main hall. Here, a biocell needs to be inserted to power up the drill control panel. Then, the ice drill can be moved using the arrows on the control panel. To position it correctly to get the achievement, move it to the rear once, left twice, then forward. Now the button that powers the drill itself will be enabled, and you can drill the hole.
Note that after the first movement of the drill has been made (i.e. to the rear), a worker in the facility will question Jensen about why he is moving the drill. The omega option "Scold" works the best, and does not generate suspicion. Options "Apologize" and "Provoke" will cause a gold-mask terrorist to go check the control room. This does not trigger an alarm and it is relatively easy to take cover from the right side of the door and perform a takedown on that terrorist while avoiding to show the unconscious body to the nearby security camera.
To get the achievement, you just need to drill the hole. You do not need to actually go through the facility via that route.