Hmm... since we have found out about Ying-yang elements, I thought about Senjuu and Uchiha as Yin-Yang.
Ying -Spiritual powerfull energy elder son possesed and it was given to Uchiha clan
Yang - Physical powerfull energy younger son possesed and it was given to Senjuu DNA
my theory:
Amaterasu - the highest and the strongest form of Fire release + Yin powerfull energy + hate(optional)
If Hashirama was hit by Amaterasu, his
full of life chakra equal yang element and
deadly chakra of Uchiha equal Ying element could cancel each other, cause
Amaterasu to turns back to normal
fire release but still very powerfull depens on amount chakra used by user to generate amaterasu. Now then:
#1th Hashirama could absorb chakra from Fire release via Mokuton cause Fire release to loose source needed to fire to exist, after having no chakra fire could simply disolves
#2th Hashirama could extend his still burning part of bodies in shape of branches/roots and put them into water or simply extend them then cut them off from his body and finally pull these branches/roots in his body
#3th Hashirama could use water release and extinguish there flames.
Conclusion: Hashirama could conter Sasuke's Amaterasu
#1th: Via Ying-Yang element my theory
#2th: surivive long enough via his very high regeneration rate so after Killing Sasuke, Amaterasu would finally dissapear.
#3th: thanks to sage mode he would be able to avoid it.
#4th: Bringer of darkness could make Amaterasu very hard to impossible to hit Hashirama
I hope I helped you
