to get the time medals, this doesn't count the time that you are busy shooting, just how long the window is open, open it up at night, go to bed and in the morning hey presto you have plus 100% power to your cannon...
@ TGuardian, for the first level, you want to get a bunch of the planes to hit them because there is weak anti-air. that along with a bunch of subs can usually beat them fast, just remember to start getting the anti sub when you see them coming.
max out your guns BEFORE you kill their base for the Yamato, then pount it with everything you have (9 guns at least) should got down faily fast if you have a good sized fleet to go with it.
the real trick is to stall it while you guns pound away.