Since Hashirama was hailed as the "strongest shinobi in his time", I could only think of 3 possible scenarios of how he got killed:
1.) There'll be no more contented shinobi in the NU who wanted Hashirama to die other than Madara. Hashirama was his main adversary. His growing hate for him was intensely depicted in the seiries. He became an avenger eventually. Thus, if Madara managed to survive with their all-out-fight at the valley of the end, then he could have a sweet revenged by killing him in the latter. How he defeated him though, is still uncertain. Perhaps, he had gained advantage from the war by succeeding so.
2.) Another possible shinobi who could beat him in a battle is Tobi. His S/T tech, combined with his agility, & intelligence are quite impressive as hell. He is such a dangerous opponent as powerful jutsu's might be useless against him. In addition, Tobi is a proficient genjutsu user. It is clearly undeniable that any shinobi who caught him off-guard will most likely be defeated.
3.) Since Madara & Tobi are aware of each other, as they can be on the same organization or whatsoever, then it's highly possible that they teamed-up to kill Hashirama. If they were to pursue with their Moon Eye Plan, the 1st Hokage will surely be a hindrance. Hence, to increase the probability of their goal to succeed, Hashirama needed to die. Should Ems-Madara & Tobi teamed-up for the battle, any strong opponents will surely be overpowered.