The correct forms are:
(i) Ты одна на университет.
(ii) Ты одна в университете.
Both variants have the same meaning, ''You are only one at the university,'' but there is a subtle difference in the flavour. Sentence (i) somewhat emphasises the ratio, i.e., 1 to 1000 or how many students study at this university. It is like a fraction: The person you are talking about is in the numerator, and the rest of the university is in the denominator. Since you put the person you are talking about to the numerator, you use the preposition ''на''. Sentence (ii) just neutrally conveys the information that the person you are talking about is unique, only one, so now the focus is entirely on the person.
If you say, ''У нас пять отличников на университет,'' you imply that very few students manage to get only the highest marks. And if you say, ''У нас пять отличников в университете,'' you just matter-of-factly convey the information that there are five students who have managed to get only the highest marks.
Analogously, there is a subtle difference between ''ты одна на весь свет'' и ''ты одна на всем свете.'' They are analogous to sentences (i) and (ii), respectively, with the second sentence requiring ''на'' instead of ''в'' simply because the world is perceived to be a surface, the surface of our planet, and people are ON the surface, hence ''на.''
In essence, ''на'' = ''on,'' and ''в'' = ''in,'' but non-native speakers need a lot of practice and experience in order to avoid mistakes in using Russian prepositions, as Russian is a highly idiomatic language.