You can't, without having access to his phone.
If you're seriously thinking of invading his privacy like that, it sounds to me like your relationship is already over. If you don't trust him, reading his messages won't make any difference.
There are two possible outcomes: You find out he's been cheating or lying to you, or you find no evidence of that being the case. If it's the latter, then you'll probably just keep searching for evidence of his guilt.
No relationship will last like that. Besides, I think that what you're trying to do is probably just as bad as whatever you think he's doing. Cheating and 'spying' are both signs that something's fundamentally wrong with your relationship.
If you really want to find out what your boyfriend's up to, and actually want to salvage your relationship, then talk to him. Whatever you're hoping to find by eavesdropping won't make you happy, but a heart-to-heart conversation might just be the key.