Discobux are the premium currency of the game, and are surprisingly a very common find. You can spend money on them if you want, but they can very easily by found for free. One common location is in the rescue missions. If there are discobux available there, they will show in the top of the screen, instead of one of the animals.
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Another surprisingly common location is in the zoo itself. Just sit there and wait and watch coins drop. Eventually a Discobux will drop as well. Like coins, they will only sit there for a little while waiting for you to pick them up. Then, if you don’t, they will disappear.
If you want to earn coins while you are away from the game, make sure that your push notifications are on by going to the options menu and checking it. You will have options to set push notifications for the first animal and the last animal to fall asleep. Put the screen on lock and have your phone on you, so that you can feel the vibrations whenever an animal falls asleep.
Your zoo will be upgraded depending on how many total animals you have. It has nothing to do with how many different types of animals you have, only how many total animals. Check your stats area in the menu to see how many animals you need in order to upgrade your zoo.
This is especially easy to do if you write down the different combinations for any animal that you see anywhere other than the farm. You can buy the Zoopedia in order to unlock every animal, but the patterns show every time that you fail a round, so simply write down the patterns for each animal, then go back later and use the patterns that you wrote down in order to get them.
This is especially important for any mystical animal that you come across, as mystical animals are the ones that will give you the most coins, and that will take the longest amount of time before they fall asleep. You won’t find out what the animal is until after you catch it, but there is only one mythical animal per rescue map.
For your common animals, simply level up their enclosures if you want them to stay awake longer. Every enclosure can only be leveled up to level 6 before you have to start freeing animals. Each new animal adds to the coins that they earn, but they only start staying awake longer once their enclosure levels up.