Rebuilding DPS Kassadin's with all the comments.

Im analyzing the possibilty of eliminating Sheen of the early build, i feel you get enough damage output from Guinsoo's Rageblade to begin your role as a DPS.


SushiMooshi wrote about of making the Hextech Gunblade earlier, I've tried it and it's really promising. Right after you get your Guinsoo's Rageblade. This gives you a boost in your full damage, in addition Hextech's slow and instant damage really improves your ganking potencial in middle game.
I found the suggestion very useful.

Berserker's Greaves were a terrible mistake on my behalf, you should ALWAYS go for Mercury Treads DPS Kassadin is awefully susceptible to CC, even though your rival only has 1 CC and its a snare type that gives you room for attack you won't be able to RW in and out of the battle as you should. (Always mean 90% of the time, there are teams that actually are full of Ezreal, Corki ... and 0 CC, pawn this team... just don't ask and eat them.

Minor Talent build change, 2 extra points in Alacrity and 2 less in Brute Force . You will find Kassa will be really AS dependant.

I'm a DPS freak, i always try to play mid carry with Ashe, Sivir, Ezreal, Tristana, Miss Fortune and every AD champ i can get because i love to take down those squishy early game and everyone late game.
Now im trying to put to test my champ development skills and design a viable DPS Kassadin.

First things first:
Hybrid DPS Kassadin was designed with the objetive of making your Kassa hard to counter, tanks won't know how to defend from you because you will deal strong AD as well as AP.
Kassa's gameplay will change a lot when you try this build: Riftwalk, Null Sphere, Force Pulse will be your "i want to get to that carry and ready to fight combo" and not your entire combo

Greater Mark of Desolationx9 build's name is ArPen FTW, you want this, you NEED this
Greater Seal of Scaling Mana Regenerationx9 well i think you could get something defensive like dodge runes, i pick this because i only max Nether Blade in lvl 10, and untill then you won't have enough mana to spam combo in lvl 6, this is my choice, you can pick anything you want here (HP seals are also a good decision)
Greater Glyph of Cooldown Reductionx9 CD red will aid you to empower your Guinsso's AS faster so i picked flat, maybe per lvl is also a good call, its up to you.
Greater Quintessence of Desolationx3 ArPen FTW again.

NEW BUILD
With help from my early readers and comentators i found that DPS Kassa had some slight defects with the old build.
1. Sheen, even though it's a great item for every hybrid dps champ, i think Kassadin doesn't depends on it as i thought, you can get it, it's fine, good and viable, BUT early Guinsoo's Rageblade it's much better.
2. Tear of Goddess, last comment said that kassa could get OOM in some battles, and it could be true, even though Kassadin can get mana from attacking, sometimes it's not enough, particullary when you are not fed and not ganking right, i like this between Chalice of Harmony because if you want you can turn it into Manamune wich gives you some extra AD.
IMO, i do not get Tear, even though it's a good and cheap item, i buy some Mana Potions every time i bluepill back to base (wich is not more than 3 times) i find it quite more viable because pots doesn't occupies another slot wich you are going to need later, and Manamune it's not a late game item.
3. Earlier Hextech's Gunblade, you gotta love the synergy with Guinsoo's Rageblade, the slow plus the 300 damage helps your burst damage and your number of hits on the target, it gives you more AD, more AP and yesSIR LIFESTEAL!
4. Frozen Mallet, a situational item that gives you extra slow but most importantly HP, and HP is maybe the reason why people do not dare to play DPS Kassa, he has a very low HP pool. Hopefully we have this item to counter that.

Notes: even though this is a ArPen named build, you are no longer seeing Black Cleaver early in the game. It is a GREAT item IMO, great damage, and a scary debuff for any enemy carry but, you are an anti carry, and most of the carrys in the game will not stack armor because it's not their role to recieve damage you know. that's why i have posponed the big cleaver for a LATE game situation, when you want to slice enemy armored tanks into pieces.




OLD BUILD

Basic Build

Gives you enough mana to hold on to untill lvl 9-10 when you recall to your base and buy Sheen
i play with 2 Health potions, its your pick
Sheen is core for HybridAD Kassadin, riftwalk autoattack will damage a lot when you do it. Why burst into Sheen before BoS, well most of the times you will get Sheen and the boots, but if for some reason you can't pick the first one, your Riftwalk gives you enough movibility in mid game
yah get this :)
YES!, while Kassadin is mostly a spam caster your guinsoo will benefit from the spam greatly, giving you a lot of AS in a fight. Your initiation combo Riftwalk, Null Sphere, Force Pulse, Nether Blade and 2 auto attacks will give you 6 stacks on your guinsoo right away. Pretty cool, isn't it?
You can always pick the shoes you need for the game you are playing.
This item gives you more damage, some attack speed but most importantly gives you more Armor Penetration
Another Hybrid item, you spamming (AD and AP) moves will heal you giving you more survability during the fight. And the slow is pretty good too, build this beginning with the cutlass for the slow as well.
You could've got Phage anytime before, depending on how fed or not you are. but this is your last offensive item you should get, increasing your Sheen to 150% damage after a cast is a good improvement.
Any defensive item will help, Banshee gives you that block spell that can save your life a lot of times while fighting.

Situational

The Brutalizer -> Yoummuu's Ghostblade More ArPen and some crit chance, a very good item, the CD red will help you mixed with the Guinsoo allowing to spam more quickly, the downside with this item is that Kassadin's doesn't have much base damage. If you are going to get this dont go for the Sheen, get The Brutalizer, followed by Black Cleaver, finish the Yoummuu's Ghostblade and get a The Bloodthrister ASAP, because now you are a full AD champ who needs Life Steal.

Wit's End Anti-Mage item, get it if you are facing a Caster team and you have to sneak by their tank(s) to get to that annoying fed Ryze or Viegar before they can combo your team down.

Malady Pretty good item when you feel your enemies are countering physical damage stacking armor, combine it with a Madred's Bloodrazor

Infinity Edge I had the feeling i needed to put this item in a ArPen build, you now you will get a lot of attack speed with the build and a decent armor penetration, its your decision if you get this. Personally i don't like it.

This makes Kassadin a great anticaster champ, mixed with Guinsoo's Rageblade AS will be brutal if targeted
This is a AP skill, you will use it to charge your Guinsoo. Take one point to begin with and max it after you max your Nether Blade
Even though it only castes for 5 seconds, 50 armor penetration points are just brutal if you have an AD build. it will take on any guy standing in front of you.
Give this skill a point in lvl 2 just to harrass and farm, don't max it.
Ulti to get in location and KIIIILLLL

Pros:

Capable of dealing a lot of damage and leaving unharmed
You can always return to a AP build while folowing this guide just mejai's and lich bane and you are all set.
When fed you are imposible to be countered.
This build can modified to make Kassadin able to TERMINATE any fed guy in the other team
I find it more enjoyable :D

Cons:

People will think you are a noob if they don't know you or the build.
Kassa won't farm as easy as he does in a AP build.
It's an expensive build

Early Game

Wether you go solo top, mid, or in a dual lane try to play defensibly until you get your core items, Kassadin's survability relys on his ultimate.

Mid Game

With your Riftwalk ready, Sheen equiped, and your boots you can go gank:
Combo this way: RW -> NB -> AutoAttack -> NS -> FP -> repeat -> Exhaust -> AutoAttack 'till dead
Farm untill you can buy a Guinsoo's Rageblade and then get the Dagger Now gank with a teammate who can CC enemies untill you can get your Black Cleaver. Now you will deal SERIOUS damage in about 3 to 4 seconds

Late Game

If you got fed = GG at 25min. If haven't you have to get some survability now. I like Hextech Gunblade because DAMN, its a lot of lifesteal during a fight, enemies will not be able to kill you, plus the AP and AD from the item are good offensibly
Keep pushing and killing enemy carries in team fights making the combo, blinking in and out of the fight abusing your Life steal and Spell Vampirism dealing good damage.
If you feel its needed get a Banshee's Veil to counter some CC, if not get a The Bloodthrister stack it and win the game.

Thank you for reading my guide, i hope you can help me with some good critizism, and some new ideas for this build. Try it, i have and it's viable and the feeling is great when an idiot says: "noob kassadin building AD" at 10 minutes, and at 25' he sends you a friend request because you are so damn good :)