A CV light cannon will not do much to a planetary POI's shields. if you are truly stuck, make a basic SV with 2 heavy lasers, rockets, or railguns (make sure you can make the ammo), and enough reverse thrust to back up in reverse. Its a somewhat cheesy method, but it will work if you're stuck. Fly directly above the POI out of range of its weapons: 4-500m in atmosphere, 8-900m on an airless moon. Point 90 degrees strait down and line up with the shield generator (glowing thing in the center of the dome) slowly descend until your cross-hairs turn red (the shield generator is usually the highest point on the POI so you should come in to range of it while being outside of the turrets) and take it out. The rockets and rail guns will penetrate the shields enough to destroy it before they drop, and the lasers will need to bring down the shields before chipping away at the generator. make sure you have at least 10x2 reloads worth of ammo, more if you're planning on taking out any of the turrets as well.

edit:
Not to mention, but planetary POIs have something like a 200% damage bonus to CVs so if you are only using light weapons, it is unlikely the CV would be able to stay in the fight long enough to make a difference

Another possible approach is to build a CV fully loaded with medium turrets and a lot of light turrets. Harden it with zeno in a long front nose with decoy gun and generator sealed inside it. Hardened steel for the rest of the ship. Also include an advanced shield. Build it so all turrets can fire at the same time as you come in at an angle.

You should have enough fire power to overwhelm the POI while most of their fire will go to your sacrificial nose. Direct guns to shoot at their guns and come in fast targeting one gun (or group of guns) at a time. Done right this can be very effective. If your shields go too low, back out and heal some then try it again, just keep pounding the POI as the xeno will take a lot of abuse.

I can take out most POI or even clusters of POIs with just minor damage to the nose of the ship.

Thanks, I dont mind cheesy methods, I usally drill with with sv under enemy base destroy their core from bellow replace it with my own and let their turrents do the job.
But this one has indestractible floor AND shield

They will ALL have indestructible floors.

Nooooooooo....... but great mod, will force me to do something else, I mean differend strategy to get to juicy core.

Any of the planetary bases with shields will have 3 cores or for a few of the largest ones (sector command) more. They are really designed to take out the shield generator and enough of the exterior weapons to land safely and clear on foot. Not to say you can't take out the cores (unless they are admin) but you will probably also take out a decent chunk of the higher end loot in the process.

That is fine for end gameish, I am still on starting planets so I try mine under so I dont destroy enemy turrents so I can salvage them for resources I cant get yet.
I like I will have to go to big advanture for quantum procesors.

What Dyspayr mentioned on his first post is probably the best early to mid game method to taking out Ground based POIs, shielded or unshielded. You can have the lasers as turrets and target either generators or turrets depending on which you want to sacrifice. Any manual weapons, you can fire the same place the turrets are firing.

If you kill the generators the turrets will stop shooting including the sentries, which really helps on the ground assault portion.

Either way you will probably lose some loot as they hide loot near generators, turrets, and cores.

I ended up digging close with mining SV then blocking two nearby enemy turrents with creating ground, then I brought second SV with laser weapons trough tunnel created by first SV, aimed laser SV at that annyoing shield and blasted it to oblivion.

OH boi they did not lie, there were indeed THREE cores, I died around 20 times clearing that POI but I got my first two quantum processors

For two Quantum Processors, you can just loot an Abandoned POI.

But consider this:
I can siege Zirax POI for 5 days.
Drops mic.
Curls into ball.
Cries.

"Another dang life lesson!"

Zirax vs Abandoned, two very different play styles. The games FPS mechanics could use some work charitably speaking, but can still be fun almost as much as frustrating once you get used to the quirks.

The abandoned play a little more like old-school first person zombie shooter; expect to be swarmed by many mobs all at once, mostly melee with a few ranged sprinkled in. They use animal-predator AI and will charge you (with erratic pathing) with little sense of self preservation. This can work in your favour if you have a route to retreat backwards while clearing the swarm, but easy to get overwhelmed. unless you have specifically modified weapons, the time to reload or switch weapons is not great and can get you killed easily, make sure to have at least one high capacity weapon like a LMG or mini-gun to deal with swarms (head shots count)
[edit: flamethrowers work well against the legacy, but they also work well against you as they have a high blast area and the enemy will close the gap quickly. Using one without setting yourself on fire is a skill in its own right].
And finally, most of the the enemies will give status effects - any and all so make sure you have access to plenty of bandages, tea, red and blue pills, casts.

Zirax bases are more of an infiltration. Almost all NPCs will be ranged and have some basic AI: try to take cover, attack while reloading. Despite having some weapon jitter built in they are still close to aim-bot accurate and can almost sense where you are... or be completely oblivious staring at a wall; roll of the dice at times. In addition to the usual machine/shot/laser gun enemies, there are the occasional rocket, plasma-flame thrower, and beam gunners. These can one-shot you unless you are running good armour: heavy or some red armour mods. bring lots of bandages, healing kits, antibiotic cream, casts and water. You will get lots of dermal burns and bleeds with the occasional broken bone. If a plasma-thrower hits you, you will almost always be set on fire - have water somewhere you can get to fast, fire is a high damage DoT and will kill fast even at full health.

In general:
have a clone chamber/medical station/tent close by
If you think you have enough medical supplies, you don't
Top up your health after every fight. Healing in combat is a hail Mary, don't rely on it.
Reload between each engagement. Switching weapons is technically faster than reloading in combat, but not by much. Empty magazines suuuuck.

... and pirates are like zirax except they WILL light you on fire so keep water on your hot bar too!