So, for my experience Arachne is one of those champ wich does good in all stages of the game, early, mid, and end game, but she gives her best at end game with this build.
She has an escape wich is her ulti, she has CC wich is her second ability+the web wich slow, and she has high sustain while in combat becouse of her lifesteal.
The way you should play this champ at least in early and mid game is to search for the right moment to strike, like a classic assasin, to ensure the kill. In early and mid game with this champ you are not going to do tons of kills becouse you are not going to have the necessary damage. But, with the right web and good teamates you can still bring home some kills without dying.
In end game it's just a train wich can't be stop, you can even go 1v5 and maybe survive. With this champ i got 4 penta kills, becouse at end game there are no other champs that can stop you. With the web you can close distance with a ranged enemy too fast for them to make you enough damage, and thanks to cacoon while they are stunned you are going to heal yourself of all the life lost in half a second (no joke), and then, after you killed him, you can just keep going, use your ulti to close the distance with the other enemy while the other skills recharge, after you killed the second dude just backup for 2 second and wait for the skills, then go towards the third enemy, melt him, get away, use the blink to close distance with the 4th enemy, kill him to, and then if you are lucky you can go for the penta. I'm not speaking about fantasy things, you can actually do this in arena with arachne thanks to the close distance.
Now lets talk about the actual build.
1)Combat boots+light blade
Starting with 1500 gold you will be able to buy the second level of the boots and the light blade, wich is the first step to get Asi. So now you almost have 2 full items, from the boots you go to the ninja tabi, from the blade you go to Asi. The start of the build is really important. Usally players buy only the boots and keep the rest of the money for later, buying the light blade will make you have 15% attack speed more then your enemies wich is huge. If you manage to get the starting attack speed camp you can become a really strong champ in early.
After the first encounter with the enemy team and after having spent all your mane, if you played your cards correctly, you should have enough money to finish Asi, wich is an item freaking OP. Some times, if you get 1/2 kills, you can even have enough money to finish Asi AND buy the Ninja Tabi.
-Asi: Asi its just a fantastic items, it gives tons of lifesteal, tons of attack speed, and even penetration, and it costs 1700 wich is nothing for all those buffs. But the strongest thing of Asi is the passive; +25% lifesteal when you drop under 35% hp. With arachne this become op.
-Ninja tabi: you take those for the attack speed.
one of the best items in the game, the only one wich gives a flat +75 physical power, and the passive is awesome too, it's what make arachne just keep going, the shield of the passive just make you basically immortal for a short amount of time. And it even gives +10% lifesteal wich is always good.
even nerfed this item is a must have if you use the crit engine. You are going to end up critting for 800 with a 2.1 attack speed and tons of lifesteal. You pick this before the other crit items becouse you can just get lucky and crit, and if you do you are going to hit for a lot of damage. Instead if you buy the other crit items first, even i you get lucky (becouse its a 25% crit) with the crit you are still not going to get enough rewards for that lucky crit.
5) Poisoned star
and now we start the shurikens. It seems like they were made just for arachne, 2 items wich gives attack speed and crit, and even more they have really good passives.
You get the poisoned star first becouse of the attack speed most of all, but even for the passive.
as for the poisoned star, attack speed, crit, physical power and the really good passive. The movement speed given by the passive will help you keep going like a train.
its most of the time situational, but if you see that you dont need the beads you can buy the Blink for extra fun. Blink behind the enemy lines and just melt a light target that doesn't have an escape. Or, as i sayd in the first section of the guide, use it to keep going at end game.
There is really not a lot to talk about arachne's skills. Even if everyone complain about the web, it doesn't really do so much, its just good for the slow and the speed up, the little spiders themself are not so useful (even if you can get lots of lucky last hit in early game (first 2/3 minutes)).
Cacoon is just op, you stun the enemy for 1.4 seconds.
The first make you almost immortal thanks to the health recovery and most of all to the attack speed buff.
The ulti is just perfect for arachne. In early/mid game you can use it to finish an enemy (you dont use it for this purpose at end game becouse no one will escape kek). In late game you will use it to escape most of the time or to close distance with an enemy, not do deal real damage. Keep in mind that this ulti gives CC immunity, this mean you can use it to escape ulti like ares's ulti, or Da Ji's ulti, or even a CC like the nox CC.
To attack an enemy just trow the web into his face, pop the other 2 skills togather and just melt him, there is not really a "tactic" or something like that for arachne.
End game train
No fear of any other gods (literally, how do you stop her in 1v1?)
Rekt by anti-healing items
1 escape every 70s
Mhe in early and mid game
Really fun god to play, you can easly end up with 20+ kills and low deaths, its not a 1 to 1 god like Ratatoskr for exemple.
Godlike for new players, no need for aim (expect for the web), no need for real strategies, and most of all new players wont buy anti-healing items.
the second build is the most belanced one. What it lacks is the lifesteal from the other build, but now you won't have problems if someone build anti-healing or if there are multiple tanks. It is a fresh spown build, i used it like 3/4 times and i ended up with some good scores, le me know how you do.