I love to play Nautilus. He is probably one of the strongest junglers at this time and people still don't know how to deal with him. Not only is he a very good tank and brings alot of utility to his team but he can also annihilate anything in his path.
I'm not the first one to build items like Wit's End on this underwater beast and the idea building him damage heavy isn't new in any way. What I want to do is show you guys that Nautilus can also be a bruiser-carry jungler, dishing out damage and making the enemy team tremble in fear.

Of course most people know Nautilus as a CC heavy tank, capable of ganking like the god he is but one does not have to play him that way. Here's a way to build Nautilus a bit different. I'm not saying in any way that this is the best build out there and it is obviously very situational (like everything) but you can definitely make this work.
So next time someone tells you that Nautilus has no dmg do me a favor and prove him wrong.

This guide will give you a little help with getting started. Please only try my build if you are open for something new and already know how to jungle at least a little bit, I won't tell you how to take Wraits nore what Blue Buff does to you, try that in a custom game, please.
So if you want to have a super fast Nautilus swinging his anchor at the speed of light (almost...) then go on!

Now to that the formalities are over, let's get on to the fun part!

Pros
tons of damage
surprise the hell out of people
super fast anchor

Cons (irrelevant)
maybe a bit squishy
your teammates might feel useless

Awesome! Let's get started!

You'll need to play Nautilus a bit different than before. You're now a bruiser and a damage dealer so get used to that. People will not expect it, so try to use that to your advantage. If someone wants to picka fight with you, don't run away all the time. If you see a chance to catch someone, then go ahead and show them the anchor.

You'll still be kinda weak in the earlier lvls. You will start out with boots and pots. Going to Blue Buff, after taking your Wolves. You'll want good help from your team, you're still hell of slow on your first clear. Now consider ganking lvl 2 if there's an opportunity (see "Ganking" section).
If you do not gank then go on as normal: Wraits, Red Buff, and so on in your jungle (you might want to avoid Small Golems early on, because they hurt)
If there's no chance for a gank at lvl 4 then go back to get your first Gold per 10 ( Philosopher's Stone or Heart of Gold)

So far it seems like the old deal, sure but you'll want to change your mind set from now on. You will farm every single little creep/minion/exp/piece of gold that you can find. Your build is expensive so you'll need to farm. If your laner goes back, take some of that farm. If there's anything in your jungle, take it.
No, I'm not telling you to be a douchebag and not help your laners at all, also you shouldn't push your lanes or anything like that but I'm just making clear what kind of a mindset you should have otherwise you'll never get your build.

Long story short: farm!, gank if you see a good chance, waste no time, farm!

I'll keep this section short. Ganking is something you have to practice and I can't teach it to you just in theory. You'll have to find out what works for you and what doesn't. You need to have a bit of knowledge about how the lanes work and when a gank is good and when not. A huge part of the process of ganking also depends on your laner. If the laner doesn't know how to react to a gank then you will not get much from it.

In general remember to communicate with your lanes!!! Ask them in the beginning of the game if anyone wants anything special, tell them that you'll gank at a certain time, if you know you will, ask them if it's good before you just run in and PING the lane at least once to make sure your laner isn't sleeping! Better sure than sorry!

lvl 2 gank:
If you're on blue side especially you will want to consider ganking top lane at lvl 2 (after Wolves and Blue Buff). A single successful gank top can win your top the lane and you will not have to worry about him again. In any case it's important to ask your laner early if he wants a gank and then again after taking Blue Buff. You should also wait a little bit so that your top gets lvl 2 aswell.
Now you do not want to pick a second skill until you actually need it. Sometimes Dredge Line can give you the kill but sometimes it will not help anything and you'd rather pick Riptide for your jungle clear.

lvl 4 gank:
After clearing your jungle you will want to gank something. By now you have every ability skilled and you are pretty strong already. See if any lane seems gankable, don't be afraid to just walk in boldly and hit them with your anchor. In most cases it will at least cost the enemy a flash, if not their live.

anything there after:
Ask your lanes, see if the enemy pushes anywhere. Don't bother to stop farming for to long but if you do gank then try to make it count. Try not to use your Dredge Line to initiate but just walk up to them, hit them once, slow them and then, when they Flash you pull them back.

Don't worry if you do not get any kills on the ganks, just go back to farming, offer your laner to back and hold his lane if he agrees.

Also don't be afraid to use your ult to initiate. It can open up possibilities quite often and just having it up all game without using it isn't good either ;).

Now it gets fancy!

You start with

Boots and 3 x Health Potion

ASAP (as soon as possible)

Philosopher's Stone and Heart of Gold

Your mid game items will be

Wit's End

If you need more Magic Resist, go for Abyssal Mask, generally if noone on your team has one, then get one!

anything that builds into Trinity Force

Glacial Shroud -> Frozen Heart

Shurelya's Battlesong

Into the late game

finish your Trinity Force

finish the Randuin's Omen

if you feel like it then go for a Phantom Dancer it's fun!

For the runes you can pretty much pick anything. Nautilus is a very solid jungler. Your first clear will be very slow however and you should get help on your Wolves and Blue Buff.

Att. speed marks help you with your jungle and it will make the DoT of Titan's Wrath apply more often -> more dmg!