Q:

How is rank determined in Valkyria Chronicles?

I've played a few skirmishes and battles in Valkyria Chronicles, and so far I've never gotten an A before. I know speed is a factor, but otherwise, even on battles which I feel went very quickly, I still get C and D grades. 
How are battles graded in Valkyria Chronicles, and how can I improve my rank? 

A:

Rank is determined by the amount of turns it takes you to finish a mission. 
For the most part, the first few missions (maybe the first 5-10 missions) can be done in about 1-3 turns. The first 4 missions (if not more) in the game are a guaranteed 1 turn finishes, it just takes time to get used to the game's mechanics and knowing how to "hit and run".
However as the game goes on, 2-3 turns max will be your "A" rank, but you'll never see a 3 turn A rank anytime soon AFAIK. Also when it comes to missions with defending only instead of capturing a base flag etc., Killing all enemy units in 1-2 turns are your only hope of getting A rank. If you follow up until the end of the time limit of the defense you will get the lowest rank in the game.
For the most part this applies to VC2 as well (I haven't played VC3 yet so I can't judge)

