A Bijuu's strongest attack is the tbb and minato tanked the Kyubi's tbb with ease when he transported it to another location with his space time barrier arts, truth of the matter is that Bee aint fast enough or smart enough to hurt Minato and his most destructive and wide range attack is useless, no way eight tails bijuu dama is better than the Kyubi that attacked konoha and Minato easily took care of that.
I'm not sure of this, just speculation but someone. Who I don't remember in another thread pointed out what I think is substantial evidence that Minato either has a wind or lightning affinity.
Why, because Minato chopped off one of the Hachibi's tails when he fought Bee and A with a mere kunai. Now ask yourself this, should it be possible for a mere kunai to cut through one of the tails of the hachibi?
So far the only other two times we have seen someone cut a tail of the hachibi was Sasuke with his chidori spear and the third raikage cut off all of its tails in one move with his hell stab technique, both times the high frequency oscillations of raiton element were used to do the job but Minato did it with a mere kunai. Now either Minato has insane strength or he has a wind or raiton affinty.
Wind is more justifiable though since his son also has wind and since wind is invisible somewhat because someone would have noticed if he used raiton since its very visible.
The is also the fact that Minato tried to stab A from behind with his kunai even though his raiton armour was activated, think about it now, Sasuke's lightning enhanced sword bounced off of A's V1 armour and his chidori basically did nothing, so why did B feel the need to stop Minato from stabbing a at V2 armour even though he was attacking with a mere kunai? B is A's brother so he would have known that a mere kunai wouldn't even phase A with his armour activated at full power, heck it wouldn't even phase him at V1 armour, so why did B intervine? And more importantly, or just as importantly, why did A thank B for saving him? Surely he, the wielder of the impenetrable raiton armour would know that a kunai is useless against him, why then does he say that B saved him? Remember that wind is lightning's weakness, B must have seen something In that Kunai that made him believe that it could penetrate A's armour and A must have seen it too ijudging by his reaction, but the kunai definately didn't have raiton armour because we would have seen it, wind on the other hand is invisible, a possible reason for us readers not being able to see it. Add to that the fact that Minato immediately chopped off one of B/hachibi's taild with that same kunai, which shouldn't be able to achieve such a feat on its own.
Minato definately used elemental ninjutsu, Kakashi said that a person becomes a jounin in Konoha when they master at least TWO elemental affinities and Minato was a jounin.
Kakashi also said that Minato planned to add his elemental affinity to the rasengan, which how he came with the idea to help naruto do that in the first place.
We have two confirming sentences from his own student that prove that Minato would have mastered two nature affinties when he became a jounin, and judging from what we have seen from his son, then and the events of his battle with the Yotsuki brothers, then one of those was almost definately wind and the other could possibly be lightning.
Point of all this is that, Minato was faster than B and his wind affinity would have cancelled out B's raiton armour with ease, since wind trumps raiton and B's strongest and wide range attack is useless since minato proved that even the Kyubi's tbb was ineffective against him when he transported it away with his space time jutsu.
B has no way of hurting Minato and Minato is way smarter than him.
Plus Minato didn't just defeat the kyubi but he also weakened it by sealing the its Yin chakra away with the reaper seal, people must remember that the only reason Naruto was even able to control the kyubi is because the kyubi inside of him is only half of what the real thing was, the kyubi that attacked konoha was twice as strong and twice as big, it even shrank to half its size after minato sealed the yin into himself, people seem to think that Minato died against the kyubi because it was too strong for him, but Kushina, his wife and master seal master confirmed it herself that Minato coould have used many other seals to lock the kyubi away without dying, she even confronted him about it, Minato explained that he did what he did so that Naruto could have a better chance at controlling the power of the nine tails, and even then Naruto still needed Kushina to hold it down for him.
Anyway my point is that if you don't have a bloodline limit like hashirama or madara, the best way to deal with a bijuu is to use sealing and barrier arts and the undisputed and by far the best at those arts is Minato, B has no way to hurt Minato and Minato isthe greatest master of the ninja arts that are the bain of all bijuu, sealing and barrier arts, and 'forensic' evidence indicatest that Minato had a wind affinity, which would be a pain to B because of his lightning affinty, also consider that Minato is one of the smartest, if not the smartest person in the narutoverse, B can never hope to defeat Minato, he's one of the strongest people in the narutoverse but Minato just has too many advantages over him, its too much of a mismatch.