Both are okay though I have read the subtlety somewhere.
In such cases, using entry to focuses on the fact that you end up in something. On the other hand, entry into focuses the process of entering. It refers to the general meaning of into.
Check out the examples:
My entry to America is the best thing happened in my life --the focus is on the fact that I entered and ended up in America. The American embassy has rules that define someone's entry to America.
The entry into midtown Manhattan (from Weehawken, NJ) is exciting: the focus is on the process of entering. Lincoln Tunnel is amazing!
Now your case,
As I said, both are okay. But IMO, it focuses more on the entrance and thus entry into is what I'd prefer.
And, both cannot be always interchanged.
My father is
into in the Indian Air Force and
And I walked right
in into the room and it was all camera and eyes on me.