This Build focuses on damage output and survivability at the same time

Boots - described later

warmogs of course increases survivability while giving more damage to her W.

rod of ages provides both health and AP increasing damage output on her W by a lot and the other spells pretty well

you will be auto-attacking a lot to apply frost so the Atma's increases your AD (Based on max health so it synergises with her W) it also gives some needed armor

the abyssal scepter works well due to your close proximity to the enemy team along with providing some magic resist.

Rabadons provides a ton of extra AP for that end game damage

Boot choice is situational based on the enemy team and who you see as being the biggest threat
(obviously you should only take 1 boots option not 3 they are there due to being options)

If their team has a lot of CC then you want Merc treads to counteract that, this does give you a lot of magic resist so this is also good against a AP heavy team

If they are comprised of mostly AD carries and the like you will want Nija-Tabi which will reduce incoming damage from them, it also provides some extra armor which rounds out the build to have close to the same resistance to both magic and physical damage.

if you want to do more damage and don't care about defense you can go for sorcerers shoes.

if you don't like the Atma's Idea i would suggest sunfire cape as an alternative as it will provide armor and will add damage to your aoe
Also Frozen Heart would be a good substitute against some major AD teams
Randuins Omen would also be another option