There's a third way to do this which I personally found much easier and more consistent than the other options, but can only be done at a specific point in the loop.
Roughly 11 minutes into the loop, Giant's Deep lines up with the gravity cannon on Brittle Hollow. If you launch the nomai shuttle from there into Giant's Deep, the barrier current doesn't load in quickly enough and you pass right through it! I can personally confirm that this does award the achievement as well.
Step-By-Step Procedure:1) Start a new loop and sleep through the first 8-9 minutes.
2) Navigate to Brittle Hollow's gravity cannon.
3) Recall the Nomai shuttle and get inside.
4) When Giant's Deep moves into the middle of your view, pull the left switch on the nomai shuttle controls to launch the shuttle.
5) Don't touch anything else, just wait.
If you timed your launch correctly, you will fly straight into the core of the planet! Thankfully Giant's Deep is quite large and has strong enough gravity that you don't need to be very precise with your launch timing. Still, if you do miss the planet, simply try again in the next loop.
I got this method from a two-minute video which you can find here:
All credit to Helix for the video guide.