To start off, Eve has a super punishable early game, she has a decent powerspike at level 4 but becomes really strong at level 6. Most games is a farm till 6 angle unless you see an available opportunity to gank a lane or take an enemy jungle camp. Champs like graves, kindrid, rengar, j4, reksai, warwick, kha'zix may try to invade you early because they are stronger than you. Those are champions you have to watch out for.

At level 6 Eve has a really big powerspike. You should aim to hit level 6 around 7:30ish, this is where you want to really look for a potential pick or gank. Usually nobody has pink wards set up at this time because its the early game and they want to utilize thier gold into other items. Getting a lead off a pick, for example, going bot lane and killing the ADC can help you keep the upper tempo in the jungle, as well as put stacks on your darkseal, your bread and butter item.

Getting objecives on Eve is super important for her style of play. She is a tempo jungler so when you have the lead you should be looking to take objecives on spawn, especially since most other junlgers in the game are afraid of eve when she is ahead. You want to try and force lane prio with your lead to make sure you can get the objecive. When you are behind you can use your invisibility to flash R+smite to steal objectives too which most junlgers cant really counter play unless they have a chogath or nunu maybe.

The mid game is where Eve shines the most, its the snowball part of the game. you have items, which especially in season 14 are really broken on her. you wanna always be looking for champs you can one shot to pull leads in lanes or get more stacks for darkseal/mejais, eve from my experince is a limit champion, if you are not confident you can kill with full combo, dont do it. One nice thing about having perma invis is that you can always reposistion yourself if needed for backline engage during teamfights or picks.

Do this is the part of the game where you wanna be looking to close out. As tempting as it can be, dont ego yourself because it takes one death to completly lose all jungle tempo. you can literally go from the strongest champ to the weakest champ in the game from one death because you decided to ego chall on things you did not need too. look to close out a game from 28-40 minutes. After that enemies will have same items as you and one shotting becomes a lot harder to pull off and you have a higher risk of dying and losing stacks.

This is just usful tips about the champ herself, her q has 2 parts to it, a skill shot and then 3 auto lock abilities after. Hitting the skillshot will empower your next 3 abilities by uhm....A LOT lets just say, so hitting it can be the difference between getting a kill or not. Her w can not only be used as a charm but also used as a slow if you break it before it fills up. its a big slow too so it can help you chase down or escape, especially pre 6. Her e gets empowered everytime you enter your passive, empowered e does max %hp magic damage scaling off your ap(it one shots tanks) it also gives you extra move speed so it can be used as a great diving tool as well. Her r has a lot of versatility to it, you can use it to be an execute, block incoming skillshots/turret shots, using it backwards to be chasedown instead of using flash, its on a low cooldown as well so its worth to use r instead of flash the majority of the times.

Another thing is to always try to keep up with your jungle camps, they are AI so you dont ever have to worry about dying to them, always keep your eyes on the mini map and move your camera around. Those are general tips i guess.

Last thing. Try your best not to die and fall behind. Eve feels really bad to play at a disadvantage. Dying can cause you to lose tempo, rendering you essentially usless.