Warrior-Assassin Amaterasu (S6.13) Arena Build

Even in Arena you need boots, if only to be able to catch up or escape back to the fountain; I'd recommend Ninja Tabi if you're going attack speed focused and drop gladiator shield completely because it's a bridge item that's usually bought early and sold for the 5th or 6th item slot.

As for the damage comment, I'm with Boogie on this: you're not going to be doing a whole lot of damage against tank with no or very little flat pen and/or protection reduction. Ich's 10 pen is like a wasp stinging you instead of a bee. Sure it hurts more, but it's still just an insect.

Not a good build, even for an assassin like playstyle.
Not buying any sort of boots in the early game is just not good. Limited mobility is a hindrance to your team and will easily allow the enemy to pick you off.

You say:
"Moderate ability attack damage"
No. You don't have enough penetration to have moderate ability damage. Most of your damage will be mitigated by the enemy's built in protections.

"Good against tanks"
No. Not enough penetration against squishy targets. Certainly not enough against a tank.

If you're new to the game, you should try playing Amaterasu as a tanky warrior, as that's her intended role, before you try unique play styles. Please respond to this thread, and we'll happily help you with this. Suke99 is a master at Amaterasu and he can give you some good pointers.

If you want a assassin like playstyle in arena (with decent protections/survivability), try this:
Warrior Tabi
Breastplate of Valor
Shogun's Kusari
Frostbound Hammer
The Executioner
Qin's Sais
Sell Warrior Tabi for Stone Cutting Sword and Elixir of Speed.
>You have damage from Frostbound Hammer, The Executioner (+ penetration), Qin's Sais, and Stone Cutting Sword (+ penetration)
>Cooldowns + protections from Breastplate of Valor and Shogun's Kusari
>Utility from Frostbound Hammer and Stone Cutting Sword