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It's not so much about farming levels as about getting your gear ready. You should make sure that all of your gear is reinforced to the amount that you want before killing Gwyn and going into NG+.
As for killing Gwyn, he can be difficult because he's fast and aggressive. He's weak to fire and magic. Lightning barely dents him. My first time beating him, I used a halberd and stayed out of his range while poking him. Long range weapons can do this.
You can also learn to parry him, which makes the fight much easier if you are good at pulling it off. There are also other tricks using magic or pyromancy.
I think I had the elite knight armor and grass crest shield. The dragon crest shield or black knight shield are also good, since they have 100% physical and high fire block percentages.
I'd suggest going with weapons that you feel comfortable using. Going into the fight with a weapon you are unfamiliar with may not be a good idea. Nor did I mean to suggest that you should specifically use the halberd. There are lots of different strategies
you can use that will depend on your playstyle and your stats. Are you a tank? High Dex or Str? Do you fast roll? Etc.
Even when beating NG+4 I still used the halberd strat to stay away from Gwyn. It's quite simple: he punishes the player for making the slightest mistake, you punish him for making the slightest mistake. Whenever he kicks or tries to grab you, hit him and
fall back. Other than that, keep moving backwards away from him while holding your shield up (a shield with high fire defense is a smart move, I've been using Black Knight Shield +5). The attack where he "hoovers above the ground" to come and stab you should
be roll dodged as it takes a lot of your stamina and might stunlock you. Being stunlocked is something you never want to happen against Gwyn or any other fast boss. Also, while the pillars are a great thing to keep between you and him if you need to heal,
don't get fooled, he does come pretty much through some of them. Learned that the hard way.