As you progress through the game you will unlock PvP battles (player vs player). You’ll be able to pick from one of three players to fight against at a time, so aside from making sure that your power level is higher than theirs, always try to make the best matchups by element. For example, if they have three fire types, use three plant types or three rock types, or a combination of the above.
Winning in the PvP mode will earn battle points and sparks. Hitting various battle point milestones will earn you prizes, to include everything from coins to sparks, to even earning rare battle creatures. Play in the PvP mode often, as much as your stamina will let you, and when you need to, use the power boosts at the beginning of the battle (150%, 200%, etc). ONLY use as much of a boost as you really, really need though.
Every once in awhile, grind through as many battles as possible and save up your speed-ups. As you progress through the game you’ll unlock new strands of DNA, such as rock DNA, and when you use it to breed a character, the rarity tier will be higher as will the initial power level. This means that it will also take longer for that new character to hatch, but when you have a full load of speed-ups (5 maximum at a time), this will kill the waiting period, or at least most of it.
Your party consists of four monsters at a time (three actives and one backup monster), but it’s best to carry more than four monsters, of all types, so that when you know what you’re up against in an upcoming stage, you can organize your team accordingly. Keep them upgraded with sparks so that you can swap them out anytime with a minimum amount of power lost.
This game, you might notice, is ad-supported, meaning that the premium currency, coins, is given out for free fairly generously by the makers of the game. Go to the in app purchase store and you will be able to earn free coins by watching advertisement videos. Eventually the videos run out, but go back later and more of them will show up. Also, coins are frequently earned in battle as rewards for victory, and in the ICL.
If you want the best chance at an extremely powerful rare creature for the minimum amount of coins spent, go to the featured store and choose the mystery box. You’ll will be able to spin for a very rare creature for the price of a not-so-rare creature, depending on which mystery box is available. Normally, it costs 999 coins for a rank 4 character, and even more as you go up the ranks.