When I build Evelynn tanky I can gain an early lead from my Damage and ignite so I used that idea and morphed it into a play style where I become unstoppable early due to kills but then unkillable later due to the tankiness and burst she still has from her ultimate ability. This build STOMPS in lower Elo.

People may wonder why I take ignite instead of flash but the answer is simple: Evelynn has permanent stealth, as an Eve player you have to be patient and tactical and to do that you can easily choose when to go in, since she has stealth you can juke enemies out due to your mobility boots, w, and stealth not needing flash. Ignite also gives that early kill potential which is what Evelynn needs for most of her matchups since she's very reliant on a gold lead and is a monster when ahead.

Early game you play Evelynn normally, an assassin. You try to influence the map AS MICH AS POSSIBLE, you control the early game and you can control if your team snowballs to the enemy nexus. If you are impatient then Evelynn is probably not for you, but if you want to demolish especially in lower elo then I highly recommend investing time into her, even though she's not meta, her tanky side helps the team because she speaks up Damage and a good Evelynn will play mind games with the enemy team so they can throw.

Pros:
High Damage Early and Mid game
Permanent stealth
Mama regeneration while stealth
Can gank from unique paths while most others can't
Cons:
Highly squishy early
Control wards reveal her
Is a champion which you need to be patient with
Lacks hard cc
Can throw her lead if she's not too far ahead by dying

Flank from behind and kill the back line in teamfights, steal the enemy buffs as much as possible so you can give your own to your laners.

Take CS from your laner whenever they are roaming / backing so it doesn't push into turret. Also when you start off the game start raptors because you get more XP and lite them with your q, then do redbuff and invade the enemy looking for another kill if they started on the other side. Always try to look for a buff steal in the beginning of the game so you can set their jungler behind.

You start off with your ultimate and then spam Q and E whenever you can, it's that simple.