How good is he at handling lasers ? Pestering him with lasers (at a safe spacing = just outside of his shffl nair range) is a good way to keep him grounded, make him get in his shield. Then take care to mix up what you're doing after the lasers / when he tries to get through : nair>shine on his shield, laser>grab, keep shooting, DD right outside of shield-grab range.
AC bair>shine and dair in place/fading away will both beat his nair clean, when you feel he's gonna jump on you.
When he's above you/on platforms, make him understand he just cannot fall on you with drill/anything : by facing away and bairing him immediately if he does, bair will always win. You can also u-tilt (wich will give you a huge punish on hit), but it's a harder commitment and could get you punished, especially if you spam it and he sees it coming.
You can basically control the pace of the game with laser and AC bairs alone : it's you who determines when he can or cannot approach you. This way you can anticipate before him when he will see an opening, thus allowing you to punish him for going in (for example fade-away dair). When you whiff a defensive option like this, don't take the habit of always shielding/rolling after : instead WD back, AC bair again, laser...
So the key word here is : ANTICIPATE. You know he's going to approach, all you need to do is to have a stong answer ready for when he commits to approach.
When he does hit your shield, like the others said before : shine OoS (I still struggle with this one), buffer roll away by holding c-stick away (avoid rolling in, it's pretty easy to catch), FH to retreat on platform sometimes.
If his pressure isn't super clean, you can be patient and wait till after the shine to punish with easier stuff than shine OoS : nair/bair OoS, WD OoS > shine, or shieldgrab (risky).