Yes Dear, Tsunade having the title Sannin makes her strong.

) didn't you even see in the manga? all of the other Kages acknowledged her and she was even noted as the 'slug princess'.
Also pain said that 'each of the sannins have their unique form' Tsunade isn't regarded as slug princess for just being able to summon katsuyu. Maybe there's a deeper explanation on that.
To tell you, Onoki & Tsunade were the only ones who have been in the previous wars and according to Jiraiya that during the second world war Tsunade single handedly attained victory for Konoha. (Maybe that's one of kishi's reasons why he had to make Tsunade live 'coz we have yet to see her full potential)
Do you think Healing & Taijutsu are the only things she can do? if that's so, why doesn't konoha make Sakura the Hokage? As i remember in the beginning Kakshi stated that when you have already mastered chakra control, you can master every jutsu.

) well, tsunade is great at chakra control so that implies that she could probably have lots of jutsu up her sleeves.