Beating the Campaign
Beat the campaign in Story Mode first. This may be difficult or quite simple depending on your approach. If you are a player that wants to keep all of your units alive for each battle, then this will be a time consuming endeavor. If you'd rather plow right through it, regardless of casualties, then progress will be faster. However, the further you get the more difficult the battles will be because of the losses you suffered earlier.
Keeping all Units Alive
Read the debriefing before each battle and survey the field closely. A good strategy goes a long way and planning out the first few moves can be crucial. Most units you will want to keep alive will be offensive characters, so it is best to take initiative and engage with enemy units you are sure will pose little threat to you. Do not leave any units in one place for more than one turn. Continuous movement, regardless in what direction, will keep your most important units safe.
Rushing through the Campaign
Use all your resources and units without mercy if you feel like speeding through the story to get to the minigames. It is as simple as moving all offensive units to surround the enemy and their base before they can mobilize effectively. You will lose some of your units (mostly infantry) but if you keep a line of defensive units at least three squares behind your men, then you can win most battles using this strategy.
Unlocking the Minigames
After you complete the last mission and watch the credits, go back to the main menu. Above "Options" you will see "Extras." Choosing this will bring you to the minigame menu where you can choose from all nine minigames.