Most dps Arachne

I don't want to discourage build-crafting, but this is just not that strong of a build for Arachne. If you're going just based on pure power, this isn't a bad build as it includes not only Transcendence and Heartseeker, but also Bloodforge, Ichaival, and the Potion of Power. You won't be able to build too much more power than that, so in that respect you've accomplished that goal.

In addition, this also isn't a bad build in the fact you're covering other core stats such as penetration (Exe is key for basic attack builds), and when you DO choose to go with a single-crit item build, Rage is the choice to make as it alone provides almost 50% crit chance at max stacks.

That said, build-crafting is more than just about raw stats. It's about understanding the god's kit and which items synergize. For Arachne, there are some things to consider. And crit isn't usually the best build direction. You're talking about "best DPS" as this is in your title, but I'm going to guess this isn't actually the best DPS for her. Multiple factors should be taken into account.

1. Power IS an important stat, don't get me wrong. Her passive gives her 1.5% added power for every 5% of a target's missing health. Higher power, higher % power effect. So you definitely want to build items with decent power.
   
   
2. At the same time, power isn't the end-all, at least when it comes to ability use. Note that 2 of her regular, non-ult abilities aren't meant to utilize power much. Cocoon doesn't deal any damage...it's an AS stim and CC ability. Web is almost always used not for the damage from the broodlings, but rather for the slow it provides to help you stick to enemies and prevent them from escaping (and the MS boost it gives you during that chase). As such, you typically want to focus on your DPS from basics, though ability-based builds can work.
   
   
3. Not sure if you know, but Arachne's attack progression is 0.5 / 1 / 1x. You're welcome to read the following chapter from my items guide which talks about attack progression and Qin's vs. crits, but otherwise, crit calculates off this progression. That first hit of 0.5 means whatever your base damage is ((base attack damage at your level + total power) / mitigations from protections), it's going to do only half that damage. Crit is double your base damage (not including additional % from the Deathbringer passive if you build it). But you're not building DB, only Rage, and this is all % crit chance, not a guarantee, so when you DO crit on that first hit, it will only deal the same amount as your normal base damage from your other hits.
   
   
4. In the end, your better option isn't crit. It's Qin's Sais. Qin's is an incredibly strong item for basic attack gods that have attacks below a progression of 1...the other big ***sassin user of this item is Kali, whose progression is similar to Arachne's, but even more powerful at 1 / 0.5 / 0.5x. Thing is, the Qin's passive bonus damage applies at the same amount on each hit, independent of the lower base damage you deal on quicker hits.

Not sure if this build is designed for Conquest or other modes, as it's not stated, but this build direction isn't optimal for Conquest. She has jungle clear issues, and so a common early-game pickup for her will be Golden Blade. Other normal considerations for her are Stone Cutting Sword, Hastened Katana, and of course Qin's Sais.

You might see a typical build in the following progression: Assassin's Blessing, Golden Blade, Hastened Katana, Stone Cutting Sword, The Executioner, Qin's Sais. Order can be adjusted wherever preferred, but typically you'll keep the first 3 or 4 items in that order...GB + HK gives you the necessary movespeed to allow you to skip Tabi. You can also drop in any of Ichaival, Asi or Bloodforge depending on preference, or if needed, Mantle of Discord or Magi's Cloak. I wouldn't worry about overcapping AS for her, since the steroid is only for 3 hits, and the higher your base AS without the steroid, the better your overall DPS.

If not for Conquest, then you can skip Golden Blade and the blessing, and you probably would build Warrior Tabi (or Ninja Tabi) in that case so you don't lose too much MS.