I think that with this list you already have a good chance of winning, it is all about match ups and making them work for you.
The most critical match up is your flying hive tyrant, which will have the sky fire special rule against his fliers. His fliers DO NOT have Quantum Shielding and are therefore Armor Value 11 from the get go. You have a greater than 50% chance of taking one of these down with your Hive Tyrant in a round of shooting through glancing (and penetrating) hits. His fliers have three hull points. One of the things this means is you must keep your tyrant in a position where it can't be shot until you have had a go at one of his Night Scythes. You must start him in reserve or behind cover so he can't be seen until one of his fliers hits the board. If you kill one of his fliers, the next priority unit for your hive tyrant, is the other flier, whatever else looks inviting and juicy. He is you only effective way of taking out his fliers.
The next issue you have is how do you remove Quantum Shielding from his big guns. Your best weapon is the Zoanthropes. If there is any way you can take three of these this will be worth it. Your Tervigons look expensive and you only need squads of 10 Termagaunts. However your Trygon making Smash Attacks is also very effective. Start by trying to take out the Doomsday Ark, after that your priority is to take out the Quantum Shielding on the Annihilation Barges. Once the Doomsday Ark is gone you should favor removal of the Quantum Shielding over destruction of a barge, the reason being ....
Your Hive Guard is effective against Barges that have had the Quantum Shielding removed. You should keep these preferably out of sight, they can still fire, or at least in cover. I would prefer to see you target barges without Quantum Shielding with these wherever possible. This is different to what I have recommended for your Zoanthropes and your Trygon.
Your Genestealers are there to take out troops by emerging from cover, there will be at least one squad of Immortals not in a flier and the Warriors that are available for assault. These are your targets.
You have one element left in your army, the Termagaunts and the Tervigons. You want to try and keep the Tervigons alive as long as possible. I suspect he will get tied up trying to eliminate your tyrant, Zonathropes and Trygon to pay too much attention to them. Consider spawning later in the game to make sure you have several troop options still alive to take objectives unless a Tervigon is down to a small number of wounds left. Taking and disputing objectives is their major function and in the case of the Termagaunts, being a distraction. A lot of people will immediately try to take a Biomancy power on the Tervigons. Dominate is very useful if you have a lot of Termagants to control which you will need to do in multi objective games.
There, that's my two pennies for you, hope you start to win a few more games.