There are a number of stuff you can do to basically progress in the game. We have listed some of the not-so-obvious ones that are nonetheless just as important to help you succeed in your missions or ultimately make you (in a sense) stronger.
Ranking Up
Ranking Up in the game basically increases the cap level of several things in the game including:
1. The maximum money you can hold (more money means the possibility of upgrading buildings and facilities to a certain extent which equates to additional stat boosts on your heroes)
2. Meaty Chunks (more meaty chunks means you can avail more help commands in the actual battles - extending your capacity to survive the missions)
3. Friend Cost (actual cost of enlisting heroes in your active team or Patrols) - when this gauge increases, you basically get to enlist stronger allies in your teams.
Battle Score
If you do well in battle, you can register a high score. Check the score breakdown after the battles to see what you can improve to get an even higher battle score when you progress.
Battle Shopping
You can purchase items that increase battle difficulty level, rank EXP rates, money dropped by enemies, etc. Try using them when you have enough friend points in the game.
Battle Teams
If you add a new battle team, it will give another team the chance to rest and recuperate (especially important on the latter stages of the game as villains become stronger and grow significantly in numbers). Also, if the chance will arrive that your first team will be defeated completely, the second one will jump in and continue the battle.
Friend Points
You get friend Points when other players use you hero (basically enlist your hero in their teams). Make your character super strong (and sellable by means of stats, equipment, and hero morph suit) so lots of people will want to use them (the game automatically adds your characters as choices for other players finding recruits of the same rank as you). You can also sometimes obtain friend points from battles.