The second fight shows the differences in fighting styles perfectly - the character you will be fighting with, Konan, is the most effective when she can fight in melee range (although she can use some mid and long ranged attacks as well), and your enemy, Sasori, is a puppeteer, fighting from a very long distance. It means, that if you want to lay any damage on your enemy, you will have to fight your way through the puppet - you have to hit Sasori himself to deal any damage. Watch out for his Ultimate Jutsu - he will shoot cube-like projectile at you, but it's fairly simple to dodge it, or you can just use your block to negate all the damage.
The most difficult aspect of this fight is to get close to the enemy - if you manage to do so, you will gain a huge advantage over the enemy. Konan certainly isn't the fastest fighter there is, but her attacks deal a significant amount of damage, and her Ultimate Jutsu is extremely hard to dodge, if you link it with your attack combos - unfortunately, this technique has a very short range, which means that you may have some problems to earn the bonus for this stage.
If you want to receive a bonus, finish the enemy by using your ultimate jutsu.