Collect as many items as possible
As mentioned, it's always good to get a ton of water that you can use to make purchases. This means grabbing as many things as you can on your runs. There will be things low, and there will be things high above too. Take advantage and try stock up and rake in the liters.
Of course, you need to be careful, as there are monsters that you need to avoid in the process. Many of them you can kill by jumping on top of them. This will also give you a nice bounce, taking you to a slightly greater height. Some enemies are even meant for bouncing off of as if they're trampolines so take advantage of this as well.
Speaking of which, I highly recommend that you try to jump as high as you can, because there may be some hidden items for you to grab. One of these are some dragon eggs, which will help you greatly when you reach the dragon's head. There are three eggs per dragon, and by having them in your inventory, you'll be able to deal more damage to the dragon. So definitely keep your eyes peeled out there because you never know what you'll find that can benefit or reward you.
See which character suits you best
Another thing we talked about are the two characters that the game has to offer. Both off their own skills, even if they seem minor. They both can unlock things like weapons and powers to give them the upper hand against the space dragons, but they already have a couple of abilities you can master and involves jumping.
For Stanley, he can essentially jump at a quicker speed, and although he only gets one jump, he can get some hang time. His hopping speed when going forward is nice and is helpful when going from platform to platform. And of course, he has the sword, if you want to use it for style points.
Sydney, on the other hand, has a nifty ability where she can double jump. This is a great way to reach places that seem out of reach. Yes, you still probably have to bounce off some enemies, but that will just make her elevate even higher which is certainly not a bad thing. And for her finishing attack, she actually utilizes her own dragon powers that she holds within, which is pretty sweet. Whoever you choose, you can't go wrong with either Stanley or Sydney.
Jump on those darn monsters
Monsters and mini dragons will be in your during your hunt for dragon teeth. You can choose to ignore them by hopping over them, or you can jump up and quickly drop down to give them the old one-two. By doing this, you'll be able to score more items which will net you more water.
On top of this, you'll be able to soar to greater heights where there will be some more beasts for you to jump on. And yes, this will send you higher. There are even some creatures that give you a helping hand of sorts by launching you forward, giving you a chance to reach far platforms which have many more items.
There are also some small, flying monsters, that will be hugely beneficial to you. By jumping on them, they can replenish your health. Make sure to time your jumps right though because they can hurt you if you aren't careful. But their ability to huge is great because, after completing one dragon, you will choose the next one that you want to run on. And when you do that, you will still have the same amount of health that you had on the previous dragon.
So, in short; regain your strength, or otherwise, your follow-up run won't be long.
Purchase items once you gathered enough water
There are a slew of things you can buy from the dude in the shop. Some of these things can really make your runs easier. However, it takes a while to gather enough liters of water to make a solid purchase. So, I would say to choose wisely when picking things.
Some of the powers/weapons you can buy can be used to take down enemies that comes in handy. Interestingly, some can only be used for certain colors of beasts. So if you've been struggling on a specific kind of dragon, and the powerup is good for those creatures, then that should work out nicely for you.
There are also things that can be used specifically for each character. For example; Stanley can either upgrade his current sword, or he can get another sword that is more powerful. For Sydney, she can have loafs of bread, that she can feed to the baby dragon that grants her powers, making her moves more devastating on the big dragons. So make sure to stock up on the water, and make some good purchases, and this will help you tremendously.