I would try to kill it immediately//very early and here is why:
If the world is alerted, wich is this case it would be, it will recieve more reinforcements, meaning killing it will get harder and harder.
Killing such a planet is easiest at the beginning, when AI progress is low and reinforcements are small so what you kill tends to stay dead long enogh to get the job done.
making lvl 4 worlds primary targets while keeping overall progress low will mean less high tech units overall.
Loosing a lot of ships in a drawn out battle at the beginning of the game is not so bad as the AI can draw less of an advantage from your losses, simply because at progress >50 a few turrets mean you are save.
If you leave it alive it will get reinforced into hell and if there ever is a cross planet attack, it will be bad news unless you have a really heavy defense at the gate, wich of course will hurt you elsewhere.
Here is how I do it:
If you can, keep a scout alive, it helps to plan.
Get tech for lvl 3 ships, bombers/cruisers preferred since they arent neutralized by tractor beams. bombers aspecially prefered if there is a shield. Starships are not an option because at this stage they take too long to build.
Build up a sizable force. If you have a target of opportunity like a resource rich lvl 1 system capture it before the lvl 4 (I tend to play a 2-3 planet start where this is not needed, but I guess it would help on a 1 planet start).
Once you outnumber them, go in and hit them hard. Bring along a mobile builder and make some cheap turrets for the enemy ships to shoot while you smash the infratructure. As usual leave the command station for last to not get evil lvl 4 raiders in your home star.
Thats it really. It works suprisingly well for me against diff 7 AIs. Mainly you cant be intimidated by that big evil IV on the map