Answer
Wa `alaykum as-salaam waramatullah wabarakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah Almighty and peace and blessings be upon His Messenger.
We’d like, first, to voice our appreciation for the great confidence you repose in us. May Allah Almighty help us to let our endeavor come up to your expectation, Amen.
Regarding your question, the European Council for Fatwa and Research states. It goes as follows:
According to a juristic rule, “Taking a lawful act as a profession is permissible unless an exception has been made by a clear proof.” Sport is basically permissible in Islam, if not obligatory. The Prophet (peace and blessings be upon him) urged his followers to practice some sort of sport and exercise that help keep the body fit, as long as that it doesn’t entail harm.
As for boxing, it is permissible if it is taken as a mere hobby to train oneself on how to practice this sport, without taking a human being as a target (i.e., one should direct the fists to a punch bag and not to a person). But, one should not think of adopting it as a profession. This is not permissible due to the great harm and untold risk it involves, especially to the body and life of the victim. Islam never allows inflicting harm on any person; Muslim or non-Muslim. This is based on the juristic rule “There should be neither harm nor reciprocating injury”.
Besides, boxing entails directing blows to the head and face. This is forbidden in Islam, according to the Hadith of the Prophet (peace and blessings be upon him), “If anyone of you fights (or, in another version, beats) a person, he should not hit him in the face.” (Al-Bukhari and Muslim)
May Allah guide you to the straight path, and guide you to that which pleases Him, Amen.
Allah Almighty knows best.