Learn what all of the elements on the board do and how you can interact with them. Crystals, for example, can restore your character's energy, while potions can heal him. Your best strategy is to destroy all the enemies early on, so you can move freely around the level. The best way to get coins fast in this game is by making various combos. You do them by, for example, bouncing off walls or immovable blocks.
Use them to deal extra damage to your enemies and gain more coins. You can also extend your combo string by using various ability cards, you just need to find out which ones you need. Whenever you see some DNA strain, make sure you collect it because they're not that common and you need them for creation of new characters. Keep in mind that there is no time limit, so relax and explore all possible options.