Starter items

Core items

Offensive items

Defensive items

Situational items

Itemization + Abilities
Hawkgirl is a great champ in the 2 jungle meta that is prevalent on Coast City. You should start with your E as the silence can make a great difference in the invade. After I like to alternate leveling my Q and E to up their damage as I feel like the increased damage is more useful with Hawkgirl than the reduced cooldown of her W(it resets after a kill or assist anyway) or the power armor from her passive. As far as the items go I build Hawkgirl as a damage-focused bruiser who can still take a few hits. I prefer to sell my marauders knife as soon as I can afford T2 of Coda. I continue until T3 of Coda and will then purchase either my Claw of Horus or Lobo's Chain. You should max whichever one of these you buy and then purchase the other as soon as you can. I prefer to follow this up with Deathstroke's Claymore which I will only get to T2 for a little while. Then I like to purchase the Sword of Beowulf as a bit of power armour will usually be needed at this point in the game. I then sell my vials and pick up a Suit of Sorrows for some more survivability. You should then finish your Claymore as the damage amp is great.

Jungling
You will want to avoid ganks before you get to level 3 as it will be somewhat difficult to actually get anyone without your W. When you gank you should try to grab a meteor and hurl it in to knock the enemy up(preferably the squishy) and follow this up with your E to silence them. Activate your W and when they try to run hit them with your Q and Q again to stick with them. If you co-ordinated well with your team you should get at least one enemy if not two. Make sure to ping your lane when you are coming in to gank so that your team can follow with CC and damage. You can make plenty of forays into the enemy jungle early as your silence and damage will make short work of most enemy junglers(especially those pesky assassins like Atomic Wonder Woman).

Teamfights
When in teamfights I prefer to dive the opposing carries as an aggressor rather than the defensive approach I have with a lot of other bruisers. Make sure to activate Deathstroke's Claymore to significantly impede the enemy. When diving in try to target the enemy blaster as they will be most affected by your silence. Once in the midst of the enemy hit them with your ult to separate the carries from the heavies and knock everyone up into the air. A good ult can swing the teamfight in your favour.

Conclusion
That about sums up my guide on Hawkgirl. If you have any questions post them in the comments below and I will address them with edits in the guide or a reply in comment form.