This is how I play Jungle Nautilus, and it is also my first guide. Don't downvote before trying it ^^

Pros
Very Tanky
MEGA CC
Very mobile late game
Floats

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Cons
Slow early game
Very mana hungry early game
You need a leash and defenders at blue

I take the runes
Flat AP blues
Flat Armor Yellows
MPEN reds
and flat AP quints

I take these runes because it is easy enough as it is to clear the jungle as Nautilus, and these runes make your early ganks OP while still going full tank.

The AP and MPEN really add up. You will have 24 AP without any items, and the MPEN will help you dish out a lot of damage.
Some may prefer to switch out the AP blues for Mana regen or MR, depending on their playstyle.

I go 0/21/9 masteries because I go full tank in the jungle. the defense makes me very tanky while I can still keep my buffs for longer and spend less time dead (which is very important for a tank)

I use these items as it gives me decent gp10 early game and makes me incredibly tanky late game. Like a brick wall. With torpedoes. and anchors.

These items also benefit the team, such as Shurelya's Reverie giving the entire team a speed boost which will often secure a kill or ensure your escape. It's also just generally fun to use ^^

The HP from the items also benefit your shield A LOT. 10% bonus hp into shield? Yes please! Makes you able to clear your jungle staying on Max HP and you can also keep up your DoT from the shield for a lot longer too, which ends up dealing a fair amount of damage. it's like an ignite every hit minus the -50% healing.

The reason I put 2 more items up there is because they are for when I'm up against strong AP. Switch them around depending on the oppositions team. If they have lots of AD? Sure get the Randuins and Frozen Heart. Lots of AP? Guardian Angel and Force of Nature! Bits of both? I usually go Randuins and Force of Nature, unless they have a hypercarry like AD sion or Trynd, then I go Frozen heart for the lowered attack speed.

I tend to max out my shield first because I like not dying, and it helps immensely in the jungle too. I grab Q at level 4 for ganks and I don't max it until last. The reason I do this is because all I want it for is the grab, the damage isn't as great as your E and it doesn't give you more survivability. I max R and E right after W.

I take smite for obvious reasons. Jungling. Nautilus can't really smiteless jungle either.
I also take flash because sometimes they flash away, or are JUST out of reach and Q is on cooldown, you can just flash up and hit 'em with your passive.

Some people feel the need to take Ghost, I don't though because I will be building Shurelias soon, removing the need for it.

Ignite = No, you don't want to try to steal kills off your carry as you're a tank. You shouldn't have to worry about them getting away because literally every single skill of yours (including auto attacks) has a form of CC. For the people who want to cut healing in half you shouldn't need to. They won't be able to heal unless it's something like Dr. Mundo's ultimate or Volibears passive. but your carry should have ignite anyway.

Heal.. it's alright. I don't use it though because I never find myself in the situation where I really need some health. I usually just pop W and be on my way. I still think Flash is a much better option IMO

All the other spells? You don't need them. CV will be on your support, Clarity is no problem because you'll have blue until Philo stone (and then you wont even need it still), Exhaust is a dumb Idea because you already have enough CC as it is. Cleanse you wont need because you will have Merc. Treads. Promote.. is stupid. period. also you'll be in the jungle you wont be able to use it. Teleport is meh if your team has lots of wards to TP to for suprise ganks (like in their bot bush)

For Nautilus Jungle I get a leash at blue - wolves - wraiths - doubles - red - wraiths - gank if possible. If not just keep farming jungle with W until you're oom, then B and you should expect to have a Heart of Gold and boots. I don't sell my Cloth armor as it later builds into Frozen Heart or Gaurdian angel.

Nautilus is extremely fun because of his skills. It's fun just making them unable to do anything at all.

When ganking try NOT to open with Q. Just waltz into the lane and try take them with your passive. If they flash away then you can bring them back with a Q then proceed to E and womp on them. If they are *just* out of reach, or someone tankier is blocking the way of your Q don't hesitate to ult them, it does a fair amount of damage, will Knock up everyone in the path and also has a fairly short CD.

Inb4 'You aren't fiora you can't blade waltz in'

Thanks for reading on how I play Jungle Nautilus. If you're going to downvote, please tell me why, I hate it when people don't like what you're doing wrong but you have no idea what it is x.x