Look at the rarity of whichever creatures you put into your party. You can see this at the top right hand corner of the card screen. The C is for Common, the U is for Uncommon, and the R is for Rare. No matter what their current statistics are, the rarer rating means that not only is their statistical and level ceiling higher, but their stats will increase more per level gained, making it so that they will be higher than other fighters relative to their levels.
There are a number of ways that you can put your army together, but when you put them together, pay no attention to their color, because the color is indicative of their race, not their element. Fighters have no elementals in this game, so all that leaves for deciding victories is numbers and types of attacks used.
Sometime in the middle of chapter 3 you will unlock the ability to switch fighters’ spots in the middle of battle instead of using a special attack. Make use of this for the purpose of targeting specific enemies, e.g. if your strongest attacker is on the left side and the boss is in the center, switch your strongest attacker to face off against the boss.
Another use is to put a matching monster onto a glyph. That’s the main point of the race thing – a glyph will pop up every so often that can only be used by one specific race, so switch the necessary party member over. Their regular attacks will be about twice as powerful for that turn, and their special attack will be anywhere between 3x and 4x as powerful (or effective, for a healer).
After beating bosses you will unlock permanent boosts (one per boss) that you can add to a party member. Make sure to always add this to the rarest party member on your team because this is the one who is the least likely to be replaced in the future. Once a boost is applied it cannot be undone; it stays with that party member forever.
Use the consumable items in the store to your advantage. All of them only cost Ether to buy – neither of them cost Valor Points or Matter. The Rune of Birth increases your chances of finding creatures on the next level that you play. The Crystal of Wrath allows you to use a Wrath attack before or during a battle. One attack uses one crystal.