ELITE CGC - NA
I'm going to preface this by saying I am by far not even close to being one of the best or even one of the better Arachne players, I'm not an expert - this is just a god I enjoy playing a lot and in Arena in particular. There are much more knowledgeable players that run Arachne main, this is just a build I've found worked for me and my play style.
This is a build I've devised for Arena play specifically which focuses on leveraging attack speed and lifesteal/healing buffing items to provide high sustain to Arachne while maintaining very high damage output capability. The thought behind this build is every action I perform that damages an enemy should heal me, and as long as I'm on an enemy and not getting dogpiled I can use the enemy to keep me alive as my lifesteal drains them quickly for health. This build does not change the fact that Arachne has a difficult time when enemies group up, but it allows me to play her and stay alive/tank damage that would otherwise kill me. The challenge is to not let the high sustain lull you into a false sense of invincibility and in turn playing dumb and overly aggressive because doing so will get you killed when playing against even non-coordinated groups.
The real core of this is Soul Eater, Serrated Edge, Vital Amplifier, and Caduceus Rod. These items are the foundation of the lifesteal high sustain concept. I'm sure plenty would argue all 4 aren't needed and that one or two would be sufficient, however for my particular play style I'm very aggressive and the combo of all 4 items have kept me alive in scenarios where I've had more balls than sense going up against multiple enemies, or an enemy that wasn't far from their group. Shoutout to @SamDaDude for pointing out in one of his videos how amazing Serrated Edge on Arachne is which turned me onto how valuable an item it is.
Y10 Soul Eater
PASSIVE - Your abilities heal you for 2.5% of damage dealt. Each time anything dies within 80 units you gain a stack. Gods, Large Jungle monsters and Bosses provide 5 stacks. At 100 Stacks Soul Eater Evolves, gaining 15 Physical Power, 4% Physical Lifesteal, and 10% Physical Ability Lifesteal.
Y10 Serrated Edge
PASSIVE - For every non-ultimate ability on cooldown you gain a stack of Cruelty. Each stack provides 7 Physical Power and 2% Physical Lifesteal.
Hydra's Lament
PASSIVE - For 8s after using an ability, your next Basic Attack will deal an additional 25% damage. Abilities that function like basic attacks do not benefit from this. PASSIVE - This item grants 2.5 MP5 per 10% of your missing Mana.
Qin's Sais
PASSIVE - On Basic Attack hits, deal Physical Damage equal to 1.5% of the target's maximum Health. If the target has over 2000 Health, the bonus damage scales up. This effect reaches a maximum of 6% of the targets Maximum Health at 2750 Health.
Vital Amplifier
PASSIVE - After healing yourself or an allied god with an ability you gain 10% Attack Speed and 5% Basic Attack Damage for 6s, stacking 3 times.
Caduceus Club
PASSIVE - Healing Dealt is increased by 30%. AURA - Allied gods within 70 units have 10% increased Crowd Control Reduction and 3% Movement Speed.
I used to place Vital Amplifier and Caduceus Rod earlier in my line up but I've moved them further toward the end so that I can build my damage capabilities quicker and snowball faster. Enemy team members will start to notice how hard you hit, and how quickly you kill by the time you start building Qin's Sai's, and just assume you're building further into power, attack speed, or going into critical chance for the last two items. By the time Qin's Sai's is complete the enemy team won't notice anything unusual about you since so far you're just a "typical" high damage output ( albeit not necessarily the absolutely most effective high damage ) Arachne.
If you build out of order with Vital Amplifier and Caduceus Rod as items 3 and 4 for example, the enemy team will definitely start to notice the unusual staying power.
Y10 Evolved Soul Eater
PASSIVE - Your abilities heal you for 10% of the damage dealt to targets.
Y10 Serrated Edge
PASSIVE - For every non-ultimate ability on cooldown you gain a stack of Cruelty. Each stack provides 7 Physical Power and 2% Physical Lifesteal.
Hydra's Lament
PASSIVE - For 8s after using an ability, your next Basic Attack will deal an additional 25% damage. Abilities that function like basic attacks do not benefit from this. PASSIVE - This item grants 2.5 MP5 per 10% of your missing Mana.
Qin's Sais
PASSIVE - On Basic Attack hits, deal Physical Damage equal to 1.5% of the target's maximum Health. If the target has over 2000 Health, the bonus damage scales up. This effect reaches a maximum of 6% of the targets Maximum Health at 2750 Health.
Vital Amplifier
PASSIVE - After healing yourself or an allied god with an ability you gain 10% Attack Speed and 5% Basic Attack Damage for 6s, stacking 3 times.
Caduceus Club
PASSIVE - Healing Dealt is increased by 30%. AURA - Allied gods within 70 units have 10% increased Crowd Control Reduction and 3% Movement Speed.