No, we do not have to "do" anything to enter His kingdom outside of repentance, which is a gift from Him anyway. As a matter of fact, and I had to change my answer after giving it some thought first, but there is actually nothing we can do to enter His kingdom. I am in the kingdom right now along with everyone else that has been born again in truth since Acts 2. This question is also a little tricky because if we are saved then it was Gods will for that to be so. This comes back down to the osas vs the "we're in charge of our own sanctification by our own power" debate that rages around here.
Is it our "choice" that saves us. Do we "find Him", or does He draw us and grant us repentance? Does He get ALL glory for our salvation, or do we get a little bit because we choose right? I am of the belief that God does it all, every bit of it and gets every last bit of glory for it. I am not denying we have choice and a will of our own, I just don't think "free will" is the best way to describe what we have. His word tells us clearly that we are a slave of sin or slave of Christ, and if you were truly transformed by Jesus blood then you WILL obey (not "have to" obey), and cannot lose salvation. I believe He loses none the Father gives Him, and He will finish the good work He started in us. If He has transformed you then your life will reflect this fact and you will work hard not to sin and to glorify Him. It's not at all like some people on here try to sell, they make salvation a "chance" and say God drops a huge burden on us when we are born again, having to obey in order to "keep" salvation. I believe we work BECAUSE of salvation therefore He gets ALL glory for it, they teach we better obey "FOR" salvation and if they make it they get the credit for obeying better than those who lost theirs. A garbage way of teaching, and completely works based salvation. A false gospel.
So to enter the kingdom I say we have to be in Gods will for that to happen, but as far as having to "do" something, then not at all.