Michelle Bachelet, who in her first term was well known for failing to fulfill promises and proclivity for creating commissions more than actually achieving things, is one of Time's 100 Most Influential People. There is absolutely nothing in the description that mentions influence.
Michelle Bachelet, who earlier this year became Chile’s President for a second time, is a courageous and committed leader — and a longtime champion of women’s rights who was the founding executive director of UN Women. Her life experience — from exile following a coup in her country in the 1970s to President — has imbued her with a passion to make a difference. She has always displayed extraordinary resilience and intelligence in addressing the toughest of issues. Her governance style is an unusual combination of humanity and solid leadership. She is gentle and accessible, yet also strong and determined. As she has said, she is “just another Chilean woman who works, cares for her house and goes to the supermarket.” But she is also “a woman with a calling for social struggle and public service.”
So "influence" boils down to passion and courage, as well as going to the supermarket. As Silvia Borzutzky and I have argued, she was hobbled because her emphasis on consensus (in various forms) actually ended up generating conflict. She's a popular president and a well-known figure globally, but I'm not sure exactly what type of influence she has.