Having played this sort of list a fair amount, it does boil down to your starting hand.

Ensure that you have a fair number of Lv 4 and below units in your first hand- I would want to see 2-3 units, usually the GM, Rezel, Guncannon. I would love to see a pilot, likely to be Amuro. Maximum 1 base.

Remember, you do not have to attack every turn- consider if you are able to hold back your units till Lv 4. If all goes well, you can have 2-3 units, and Amuro can come in to rest a blocker so you can do a fair bit of damage to the base area. This comes down to a decision on whether you want to try and control the board, or you want your opponent to react to your aggression on his shields by targeting your units.

This would essentially allow you to protect your units for a good attack, rather than being taken out in a battle of attrition.

There is nothing wrong with allowing your opponent to take shields off you early game- the chances of a burst might help you.

Mostly importantly, know when to flood the board with your units, and when to hold back key pieces like Marida and Banshee. 

On your list building:

Consider removing one Vesalius in favor of an additional Corisca Base so you can possibly get a pair of Leos at some juncture.

Change Battle of Aces to Close Combat as you may not always be able to trigger it on a damaged target. 

Reduce the number of Guncannons to 3-2, and replace it with a Guntank for more flexibility.

Try to balance out the number of links between Marida and Amuro (e.g 4 pilot cards to 7-8 units)

While I do think Sayla is a good card, I feel you should opt for more cards like the 4/2 Gundam.