How do i beat anivia?

By hitting her until she has 0 HP.

Get close to her and she's dead, most of the time very squishy.

Assassin Duh

Same way you beat graves.

early on, wait till she wastes her Q, sidestep it, watch her use it on minions, etc.

after that, trade with her. Her damage comes from her E procing the bonus damage from her Q or R. If she does not proc this bonus damage, then her E damage is mildly average at best and it contains no crowd control at all. take advantage of this on pre lvl 6 anivia and the fact that she has no mobility.

After 6, you can still wait for her to waste her Q and to some quick trades while her skills are on cooldown. let her push a bit and get her to waste her wall and ult on you while your jungler comes in from the side and ganks her. her cooldowns are mildly long so she probably won't have anything else to fight with. she relies a lot on her E burst for damage and does not have any significant sustained damage other than her ult which, If i remember right, will get canceled if she gets stunned.

by not sucking...

get good