You are not going to be able to achieve what you are setting out to do because there is no way that you are going to be able to see your boyfriends phone and the activity on it on your phone or on your home pc. You are going to have to accept that you are either going to have to trust your boyfriend or simple ask to see his phone when you are with him.
· Don't search online
Not online is the action of hacking someone's phone illegal, but you may get in trouble if you search online for a way to do it. There are always going to be websites which the police are watching to ensure that the actions are not going to be carried out, so it not going to be worth going on websites and trying out the instructions as you don't want to be in trouble because you didn't trust your boyfriend.
You are going to have to accept the fact that his phone is his phone and you are not going to be able to hack into it. You can go on it when you are with him but you cannot see what he is doing from your phone. Don't make a mistake that could affect the rest of your life because you want to see what your boyfriend is doing on this phone.