She is defintelty worthy to be a Sannin.
1) Chakra control and manipulation. She can do both at insane levels. Her strength is much greater then Sakura's who chakra control is already noted as excellent how much better then is Tsunade, plus she gathers chakra due to her seal on her forehead which is apparently a unique jutsu to her. to be able to heal everyone in a village with her chakra is a big deal Konoha isn't a small place, nor is itsd population small.
2) She is a medical ninja of unequaled caliber (making posions, Rock Lee's surgery, etc) and if you remember back to when Sakura fought Sasori they elaborate on what it takes to be a field medical nin. Of them she is the best.
3) Chakra capacity. Depending on your abilities determines the strength of the kind of summons. That slug is huge and has many abilities (acid for offense, healing and communication abilties etc) as notes her chakra capacity.
4) the reason the 3 of them were called Sannin to begin with was because at the time one of the most powerful and acknowledged ninjas of the time (Hanzo) said so. That be like if the 4th Hokage had declared someone a serious threat youd bet they'd be recognized.