If you have them, use drones to easily break the sheilds. If not, use concentrated plasma fire. Beware of plasma bouncing back at you, so fire from max range. They seem to break if you deal enough damage inside of a certain window, so stuff that fires slow or damages over time doesn't work well..

You can also turn down the difficulty, which makes destroying the shields significantly easier. I couldn't do it on normal difficulty with 2 lasers and several L2 maxed fixed guns and 20+ seconds of concentrated fire, which most posts say is more than enough.

All you need is the gravity gun and something to set off one of those exploding cores floating in space near the shielded boxes. The cores need to be touching the shield . When you keep charging the gravity gun (creates that swirl in space) it acts like a big magnet that you can move stuff with.

Shoot the cores with the gravity gun to get them roughly in position. Then keep the gravity gun charging the entire time while moving the cores closer to the shielded boxes. You will notice that the cores will follow that big swirl and when the swirl is close enough it will pull in the boxes and keep them together without the core exploding. Set off the core and them destroy the box to get inside.

Don't forget that there are additional cores in the debris fields next to the planets

Screenshot of the setup. You can see the blue swirl from the gravity gun still actively holding them together.