Boomerang:
Zair is pretty good at neutralizing boomerang. He's going to be in more lag from boomerang than you will be from zair. Plus, you can jump forward with zair and gain more stage control.
If you like being cheesy, you can reflect his boomerang with fsmash. It can give you stage control, catch Link off-guard, and even push him off the stage in some situations.
Arrows:
I've found the most success from just jumping over it. If you're far away, you can just react to him shooting the arrow.
If you're closer, you can jump while he's charging and go in to punish him. He has to let go of the arrow and wait for the arrow shooting animation before he can do anything, so you basically get a free opening.
Bombs:
You can absorb the explosions with PSI Magnet. Catching the bombs and then using them to heal yourself turns bombs into a liability for Link, and in most cases, he'll probably throw much fewer bombs after you demonstrate your ability to eat them.
Link's close-range attacks require smart use of your shield. He wants to catch you in the air with up tilt and up smash, so I would recommend staying grounded when you're close to him. This allows you to shield these moves, giving you an opportunity to beat him up. It all comes down to how well you can use your shield.
I don't have a whole lot of experience in the matchup, but this is what I have picked up from the few games I have played and videos I have seen of the matchup. Speaking of which, this video should be helpful for illustrating some of what I'm talking about:
https://www.youtube.com/watch?v=ftheDBNwJHU