I don't have the 1000 kills, but a good tip would be to use one of the battle time increasing tactics. That way you can get 10 more minutes in a single battle. You should also fight against an enemy with a large number of troops, logically this means more troops for you to kill.
You also need to be efficient when attacking, if you want to take down an officer then kill their support troops first otherwise they run away. This also applies when taking over bases, before taking out the base captains kill their troops.
Draw out the fight for as long as you can, you might want to choose a Defend mission so that you don't need to worry about the time limit and can just keep on killing. And put your allied officers all in your main camp and use the defence command so they don't go around stealing your kills.
Hot off the presses, apparently you can get the level 4 weapon by finishing a level within 1 minute =o