I watched the replay, did you save the game before you exited?
I did notice that your attacks were organised and it looked like you had made groups for each unit type. There are two areas that need to be looked at,
1. You need more units in each attack especially at the end.
2. Targets need to be prioritised for example when you sent your mutalisks to attack the terran supply depot their turret open fired. When this happens, switch targets quickly to limit damage of your force. Always take out the shooting targets first then return for the rest.
If you saved the game, try building...
1-2 squads of guardians
1-2 squads of mutalisks
just 1or2 overlords
A sizeable ground force consisting of
1-2 squads of hydralisks
2-3 squads of zerglings
(Alter size of attack force if you can. more is better)
Select your ground force(s) for each squad press the attack croshair in the right hand pane and select the middle of the terran base. (make sure to click attack and select a blank area) the ground force will charge the ennemy and attack by themselves.
After you send your ground force off...
Tell your Guardians to do the same as the ground force by using the attack command only send the guardians to near the command centre.
You need to protect your guardians, select the mutalisks and use them to attack any hostile forces that attack the guardians.(use the overlords as detectors)
This should leave your enemy battling on two sides, and will struggle to allocate sufficient defence.
You are doing really well,
let me know how it turns out.