How can I defeat a Cardinal and their orb?

At a relatively early point in the main story I'm meeting a Cardinal, and it didn't go well for me. I did see one a bit earlier on Eos, but I assumed I had entered a bit too high-level area accidentally and reloaded.

It seems that I can only target the Cardinal's Orb, and even then once I destroyed it, it just appears again shortly after. I'm out of ammo, and the orb is still there.

Are there any special rules about the Cardinal and the Cardinal's Orb? Can I prevent it from respawning/regenerating? And how do I destroy bot it and the Cardinal?

While the cardinal has the orb/shield out, you cannot hurt him. You must destroy the orb, and then he has a small window where he can be damaged. Take this time to deal as much damage as you can, you may have to repeat this process a few times.

If you find yourself running out of ammo just on the orb, you may have to find a better gun or target the orb better. You cannot shoot the orb through the shield around the cardinal.

Also, I recommend staying at range, when his orb is up he has an instant death attack that he can unleash on you if you are too close. Assault rifles are probably best unless you are really good at aiming with the sniper rifle.