Bonus hunting might sound like a pretty suspicious term, but it’s not illegal unless you do it in a way that is in contradiction with the terms and conditions of a bonus you have accepted. These terms and conditions are not there just for show, and if you are found guilty of breaching them, the consequences could be serious.
However, taking advantage of betting sign up offers is in general completely legal, and exactly what the betting site in question wants you to do. Be sure to read the rules of any bonus before accepting them, and try to make the most profitable bets you can while abiding with them.