Yes it's possible...but it depends...you might need to study about 20-25 hours a week (or maybe less if you're living in an English speaking country or if you learn really quickly)
Cambridge English say:
"It takes approximately 200 guided learning hours for a language learner to progress from one level of the Common European Framework of Reference (CEFR) to the next.
For example, a candidate who has passed B2 First (previously known as Cambridge English: First), aligned to level B2 on the CEFR, might need approximately 200 hours of lessons and supervised study to prepare for the C1 Advanced (previously known as Cambridge English: Advanced), which is aligned to level C1.
However, there are a number of factors that can affect how long it might take you to achieve your desired level of English, including:
your language learning background
the intensity of your study
the amount of study/exposure outside of lesson times"