Hello fellow League of Legends players,
Before I say anything else I would like to thank and shout out @Whobick for his Eveylnn guide that really brought Evelynn back to being a viable champion for me. I had previously loved playing her in Season 6 but stopped because she wasn't very good then. But even though she still needs a buff, Whobick's AD Evelynn build (I used to play her AP) was amazing and it worked! However I have changed quite a bit and thought that it was good enough to bring out my own guide. While Whobick's guide may be better in some situations, I think that mine really shines through withstanding that you don't encounter very specific champions. Please give @Whobick the credit he deserves for the inspiration for this build, without him I likely wouldn't have ever picked Evelynn up again! With that said lets get started with my build for the Unseen Huntress.
I have been playing League since about the middle of S6 and nearing the end of S6 I discovered Eveylnn and the great fun one can have playing her. While I did stop playing her, I recently started again in a new way after seeing another guide on this site. Previously I played her AP, but as someone who's played both, AD is much better! She can completely destroy an enemy team if played right and any player can become a hard carry as her in no time. To her, tanks and squishies meld into one thing, a target to be eliminated in a flash, and then to disappear into the night. With that said, lets get started!

This is quite simple, standard Summoner Spells for any Jungler, however there are a few things that you should know. Firstly Smite is a must, you'll end up having Challenging Smite for most of the game, but what matters is that you always use Smite when you have two charges on it. This way you can clear camps faster and you always have one to use on the epic monsters. Of course this is more a mid to late game strategy, however it's still important. Flash will give you an even better escape, as Evelynn has her W but no hard CC. But Flash will become really helpful when engaging. Due to Eveylnn's large detection radius, it is quite difficult to launch an attack without the enemy team being able to launch a counter attack before you eviscerate them. Flash will allow you to instantly appear next to your target(s) and deal as much damage as possible, while limiting the damage you take. This will improve your sustain in battle against multiple opponents.

You should always start your game with Hunter's Machete and a Refillable Potion, as these will be greatly beneficial to you, providing the damage you need for fighting creeps.
Your first item in this build will be Skirmisher's Saber with the Warrior Enchantment. You'll have this for the majority of the game and as a Jungler it is important that you rush this. The damage and CDR that this gives you will be exceedingly useful, improving the speed of your Camp Clears and Champion Kills. Remember, as Eveylnn you are a diver, your sustain isn't the best. Your power comes from the speed you can destroy your opponent's health, while limiting the amount of damage you take yourself.
Next you will build Boots of Speed. Due to your wide detection radius you need to be within killing range between the time they notice you and the time it takes for them to attack. What better way with some good consistent speed? Plus the slow resist will be of great help against those with a lot of soft CC.
Now you should be building Titanic Hydra as it's Health will improve your survivability considerably and its Damage and Cleave will help with taking multiple targets on at the same time, whether they be Champion or Minion/Jungle Monster. The increase of Health Regen is a nice little bonus that will allow you to stay out in the field longer, if not all the time in battle.
Now it's time for Trinity Force! This can be considered the most important part of your build because of all the different things it gives you. Increased Movement Speed, Attack Speed, CDR and Attack Damage will allow you to eliminate your foes quicker and easier. Increased Health and Mana will allow you to stay out in the field fighting for longer boosting your performance. Plus the passives Rage and Spellblade will increase the amount of damage you do and decrease the amount of time it takes to do it.
Now it's time for Dusk Blade of Draktharr and this is the beginning of your quest for Leathality. This'll give you even more AD and a good bit of Leathality, as well as adorning you in a plethora of passives that will make you a force to be reckoned with, cancelling out wards, increasing your out of combat Movement Speed and increasing your damage every time you come out of being unseen. That means any time you engage you'll do significantly more damage than expected.
Penultimatley you build Youmuu's Ghost Blade. This'll give you even more Leathality, Movement Speed out of combat, Damage and it'll cap off your CDR. But wait, there's more! It'll also allow you to activate it to give yourself even more increased Movement Speed for a short while and ignoring unit collision as well.
Now normally that would be the end of it, but no, not in this guide. Now when you attain around 1800 gold you will sell your Jungling item and buy Death's Dance. This'll give you more Damage, keep your CDR maxed out and will allow you to heal on hitting your opponent every 3rd hit and turn some of the damage you take into a bleed, allowing for you to sustain in combat for longer.

Your entire tree hear is designed to increase the chance of you killing whatever target you set you eyes on. This is because Evelynn is unfortunately a very broken champion and in a bad way for those that play her, she is meant to be an assassin but due to her abilities and stats has been adopted as a squishy diver. As such the chances of you dying when you engage is very high, so you need to ensure that you keep up with levels and always gets a kill when you battle. Standard Cunning tree build to ensure that you make the most out of EXP and buffs, while allowing your E to become even more devastating. Ferocity to improve both your basic attacks and the abilities that come with it.

The Attack Speed and Attack Damage here will increase you DPS significantly, while the Mana Regen will allow you to sustain the jungle environment and increase the chances for you to be able to engage at anytime while farming.

You want to have your Q maxed first because this is both your main farming tool and your main ability in pursuits. It's low cooldown and cost allows you to spam it and clear waves and enemies quickly.
Next you want to max your E as its high damage output and Attack Speed bonus will prove deadly for anything that gets close to you.
Finally your W is great for maxing late game, as it will allow you to go to and from base and anywhere else on the Rift quickly and before this point your other abilities are far more important.
Your ult should be bought whenever possible and is a great tool for engages so be sure to pop it whenever you engage on enemy Champions but never on creeps or minions.

As stated earlier your Q is a great tool for clears and pursuits. It allows high DPS with its low Cooldown and Mana cost, thereby allowing for good clears of the Raptor and Wolf camps after your first or second back. Whenever you engage anything you should spam the living hell out of this as it auto targets whatever you target.
Your W is great for getting places fast, whether you are charging at people or camps, however it is important to remember that this cancels your active invisibility so you should allow for time to return to invisibility before you get close to the enemy or important camps (enemy Blue or Red, as well as Drake and Baron). Also its cleanse is great for a quick getaway.
On the subject of your invisibility, it goes without saying that you should always stay in this state until the moment you engage on something. Your invisibility is your greatest power and you should use it whenever possible.
Next, your E is your highest damaging ability so this should be used on the toughest monsters in multiple monster camps and the single opponents (camps or enemy Champions) as soon as battle starts. The Attack Speed boost will increase your damage output and therefore will end the battle as soon as possible, ideal for someone as squishy as Evelynn.
Finally your ult is best used on as many enemies at once as possible. The more champions it hits the better the shield it gives you and the more enemies slowed, and thereby weakened, for the kill.
Flash makes a great tool for engages as it covers the radius of your invisibility easily.

Evelynn uses standard jungle pathing and shouldn't deviate from this at the start of the game. Start Bot-Side, you MUST have a leash, then go to the following camps depending on whether you started Blue or Red:

Blue - Gromp, Wolves, Red, Top-side Riftscuttler, Raptors then back.
Red - Wolves, Blue, Gromp, Top-side Riftscuttler, Raptors then back.

After backing where you should aim to gank where ever possible but do not force a gank. If no lanes look good to gank first get vision on enemy blue and red so you will know when they will come back up. Then if there is still no opportune ganking moment go farm whichever camp is closest. DON'T DO KRUGS. They take far to long and take off far to much health to be worth doing till later in the game. Remember farming should be your priority until you start building Titanic Hydra so don't feel pressured by flaming teammates to gank unnecessarily.

As a squishy jungler you should always gank a lane when your team is still in it, unless the enemy team member/team members are below a third of their health. When fighting the enemy jungler ensure you have a health advantage before the fight begins and that you end the fight as quickly as possible to avoid other teammates coming to help him.

So that's Eveylnn Jungle. If you take away anything this is what it should be:

AD Eveylnn is far better than AP Eveylnn and you so ignore the ignorant fools that say otherwise.
You are a squishy diver, so the quicker the fight the better.
As a jungler you are no nobody's ***** so don't let anyone treat you like one.