If I start doing Vipassana now, how long will it take me to achieve Nirvana?
There is a lovely zen saying, a dialogue between new student and master:

"Master, if I put in great effort every day to attain awakening, how long will it take?"

The master replies, "20 years."

"What if I work really really hard?"

The master replies, "40 years."

Wanting enlightenment is paradoxical, because enlightenment is the absence of defilement, not the presence of need.

It would be of great benefit to study the six perfections.  You may find this reference useful: http://www.rigpawiki.org/index.php?title=Six_paramitas

Often people assume enlightenment to be the result of something. If you are happy following causes and their results, then practice the six perfections as much as possible.  You must ultimately pair them with wisdom which transcends conceptuality in order to arrive into a state which is beyond.

It will greatly depend on your attitude and your motivation.  Thus, I encourage you to study the Buddha's words and keep a superior motivation.

No one can guarantee for you how long it will take, and when you "get there" so-to-speak, there will not be any conventional sense of time to speak of, so instead of asking "how long will it take" we should all ask "what can we do to accelerate the process?"

A skillful question is one which illuminates the how.

If you come with great faith in the teachings and practice with a single-pointed mind, freedom shall dawn.  Until the gravity of our imperiled situation in samsara is seen for what it is, benefit yourself and others with study and reflection.

One aspect of enlightenment is freedom from doubt.  Clear away all your doubts with the stainfree mirror of the teachings.  The Buddha proclaimed that "in the future" [in this era] to come face-to-face with the teachings is the same as coming face-to-face with the Buddha.

At any rate, even if someone told you that it will take 3 long aeons to come to awakening practicing diligently every day all day, what is that in comparison to an unending cycle of dying and being born?  What is 3 long aeons in comparison to the nonceasing spin of the wheel of life?