What items can you build on Nautilus to keep him tanky but allow him to deal damage, like a bruiser?
None of his damage scales from HP (only his shield), everything is AP.
There aren't really any good AP defense items, so what do you build?
Build AP and get deleted or build tank and just CC with no dmg?
Serious answers/itemization
As someone who still "kinda" plays AP tanks mid, I can probably answer this quite well. Depending on the matchup, you'll often want to build things that offer cdr/hp/AP. Things like roa help a bit, protobelt is surprisingly nifty should you want to go for proto-auto cc chains onto people, while liandrys is another one of those "sleeper items" that makes his E quite annoying to deal with. I also hardly find this thing serious, as you're literally asking for an AP carry build that also makes you tanky (which if that's the case, feel free to share with everyone else, as AP mids are pretty terrible right now).
Someone with high magic base damage deals damage with magicpen. So you kinda want items that give more damage and tankiness. Sunfire Thornmail Abyssal is very good cause it amplifies your damage by a % including the damage of Sunfire and thornmail Then pretty much full tank
Greedy options would be sorc shoes/liandries. They amplify nicely your damage but don't grant that much tankiness. Probably fun, though Nautilus will likely not be a great duellist anyway, but are less efficient than just Building full tank and peel your adc overlord
Ps: yeah I forgot cdr can be good too. Protobelt? Frozen heart? Iceborn gauntlet?
My build for him is
Hybrid pen marks Armor Seals MR Glyphs Ap Quints
If its a norms I go ROA-TRINITY into full tank
If its ranked I go 
Abyssal Scepter/RoA (one or the other) and Landry's Torment are both good damage options.
When i go 
i rush a
then a 
into a 
and HOLY COW ITS POWERFUL.
Max your Q
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Abyssals with a liandries is my preference. You won't be out damaging their adcs but they will feel it. Iceborn can help but it's generally overkill with all your other cc.
I used to play him top a lot and would get roa first or second item. After that, just maxing cdr while building tank allows him to deal a significant amount of damage. If you happen to get fed, Liandry's can be a good choice because he permslows and the stats are pretty good for him.
