In the manga Chapter 554, Naruto notices a prominent scar on the Third Raikage, which leads him to think that if the Hachibi managed to inflict damage, there's no reason why Kurama's chakra can't. But it turned out that it was the Raikage's weakness that hurt him. Using this information, Naruto managed to defeat him.
Could someone explain the nuts and bolts?
After talking to Gyuki (Hachibi), Naruto guessed that the scar on the Third Raikage chest may have been made by his own Jigokuzuki (Hell Stab). Based on that, he prepared a plan to make the Raikage stab his own chest.
He went into Sage Mode, prepared a Rasengan, and ran towards the Raikage as if to hit him head on with the Rasengan. The Raikage too ran towards Naruto aiming to stab him with his One-Finger Nukite.
Naruto's Sage Mode allows him to better sense the enemy, so he could dodge the Raikage's finger at the last moment. It also give him better speed, so he could quickly redirect his Rasengan to aim at the Raikage's elbow, before the Raikage could dodge it. This impact bent his elbow causing his attack to pierce his own chest.
This might explain the sequence of events:
On Naruto Manga Chapter 555:"Contradiction", Naruto used the Sage Mode to defeat the third Raikage. After talking to the Eight Tails, Naruto realized that the pierce in his chest was made by his own technique (The Hell Stab) thus making his weapon more powerful than his armor.
See picture below:
Naruto on sage mode can react on split seconds and he was aiming for his arm to redirect the attack towards himself.
