On the main menu screen, select the first icon (resembles a gear) and select "Redeem Code" (looks like a white computer). Then, unlock the following cards in your Deck Builder by entering the corresponding codes:
Keep all lanes defended whenever possible to avoid giving your enemies a free hit. If you do have leave lanes unguarded, make sure they're ones that will result in the least possible damage as a result.
Make sure your available landscapes and creatures are a match, so you have somewhere to place those precious creatures that will allow them to defend you. Otherwise, landscapes and creatures you possess could be worthless. Make sure that your available heroes also match.
Take out any weak foes asap. Doing so grants you another point of access to your target. It could be enough to let you win without worrying much about the bruisers.
Revisit old missions to grow levels, open deck slots, and to earn gold and additional cards. All of that can help you if you're having trouble with the next mission.
Don't be afraid to build your deck using a lot of overkill cards, since there's no real penalty for doing so.
Avoid disabling the Battle Wheel until you give it a proper chance. It provides some great boosts to damage, defense, and counterattacks, provided you tap it before the time expires. It's probably worth the extra hassle.
Aim for the Albebraic Chest when you spend precious gems, not the more affordable Cool Chest (which offers rewards you might find elsewhere without making that investment).
Craft frequently and right after you unlock recipes, even if you don't necessarily need the superior cards at present. It's never a bad idea to have some waiting in reserve.