Despite what some others have said here, I actually think Pursuer is one of the best examples in the game of locking and and circling at close range not being the optimal strategy. Pursuer has too many wide tracking combos and guard crush moves for that to work well. Not to mention that he also has moves that are best stepped to different sides.
My tips:
- Don't stay too close
His move variety at a medium to long range is the easiest to bait and punish
- Watch for the glowing blue sword of doom
You can't block this and it has a deceptively long range in the direction of the thrust, but it tracks sideways poorly compared to some of his other moves. It's best side rolled but can be avoided simply by circling toward his shield hand if you feel brave. As a bonus (for him), if he hits you with this, you get Cursed and he actually gets new moves that make him harder to fight. Don't get hit by it.
- Learn his moves
It's a little obvious, but they all are fairly telegraphed and can be evaded with practice
- Don't get greedy
Even his biggest moves don't have enough recovery time to allow you to get more than a hit or two ion safely. One or two quick swings OR one heal timed immediately after a dodge are all you have time for
- Don't heal just because you have to
I know it can be tempting when you're low on life but only heal when you are either really really far away from him (not likely to happen, he is the Pursuer after all) or instead of an attack after dodging/blocking one of his moves/combos.
- Learn to roll
Rolling is harder in DS2 than in DS1 so there's a little more technique to it. Vertical attacks can generally be dodge rolled to either side. Horizontal attacks, however, can't reliably. For horizontal moving attacks, it's almost always best to dodge against the grain of the swing. For example, if the attack is coming from L -> R you'll want to dodge towards the L. This maximizes the invincibility frames on your roll by having you "inside" of the attack for a shorter period of time given that it's moving one way (towards the R) while you're moving the opposite way (towards the L).
- Be okay with finding him tough
Considering how early you can fight him in the game and how tough he actually can be compared to even later bosses (and considering he's actually totally optional), he is actually legitimately difficult. The upside, though, is that once you know how to fight him you'll have successfully learned the tools you need for almost every other challenge you're going to face. The rewards for beating him are very good (a great ring, a great weapon/shield/armour set, a "shortcut" that actually allows you to skip one of the other bosses that people generally hate) so beyond the learning process it's worth the effort.
Some of his moves:
- Shield bash
He'll only do this if you've got a shield equipped and are holding it up. Blocking it is possible but it will totally drain your stamina and stagger you. Don't block it. Instead, roll towards him or towards his shield hand to evade it.
- Shield up charge
He raises his shield in front of him, hovers and flies towards you then attacks with a vertical sword slash. With the right timing and direction, you can actually just side walk around this to his shield hand side. I prefer to roll just to be safe. You want him using this move as much as possible because it's easy to punish and he generally only does it when you're at medium to long range. You may be tempted to back roll if you need to heal but it's safer to side roll as the vertical slash he does at the end has deceptively long range in a straight line in front of him.
- 3 hit combo
This comes in a few varieties but all are generally treated the same way. He usually starts with a horizontal slash, then does a shield bash, then a third attack that's either a slash or a dive attack. For the slash you can block but a roll is better. Roll towards his sword hand. You need to roll the shield bash. Roll towards his shield hand. If he does another slash, roll towards his sword hand. If he does the dive, roll towards him so that he'll fly over your head. The timing on the third attack is a little delayed so it may take a few attempts to get the timing right.
Hope that helps.