This didn't unlock using console commands to trigger the mission stages.
What did work was...
Prepare yourself:
tgm
player.additem 000e6b2e 500
player.additem 000BD56F 1
Head to the exterior of the vault:
coc QuincyQuarriesExt
There are ghouls, so you may want to:
killall
Head to the marker underground which takes you inside. There are ghouls trying to break into the vault, kill them and enter.
There are ghouls inside the vault, kill them and follow the instructions to get inside. You'll need to activate a terminal, take a control board from a ghoul, activate a workshop and then use it to delete material blocking your progress.
You will then meet the Overseer. Talk to her and follow instructions to trigger the mission Explore Vault 88. She'll need you to kill the feral ghouls in the area first, make her an overseer terminal, and turn on the vault radio beacon.
Once the mission has started, burn through enemies as you follow markers to find workshops, locate the control boards, and activate each workshop.
After the third one, the achievement should pop.