If you want to make more chests drop with a greater frequency so that you can earn either more coins or more relics, the best way to do so is to slow down the fight. Stop tracking down enemies; instead, defend the gate closely, let them come to you and attack them. Once you are down to one or two enemies in a round, it will be easier to defend against them (especially because they jump back all the time) so you can then rush over and collect the chests that you haven’t opened yet.
In addition to earning free gems with the quests, you can also simply find them from chests, as well. They will drop randomly and they will be very rare, and if they do appear it will be one at a time. Some of the relics that you collect can cause them to appear more frequently, though. Some of them will even increase the amount of gold that you earn per coin that you collect.
Bosses can be especially tough to defeat. Use your power ups when the bosses come around so that you can get rid of all of their underlings quickly. Then you can focus on the boss. Keep hitting them and keep them out of the way of the gate because if they get stuck over the gate, they will cause the dragon to rise again. Use the critical hit power ups heavily when you are battling a boss.
Starting around world 5, minibosses such as the big pumpkins will appear (on round 5-5 in this case). They won’t move much, but the real issue is the underlings, such as the little pumpkins that they spit out, the flying bats, and (on round 5-9), the other monsters. Fight conservatively and defend your gate. Don’t stay too far from it, even letting coins disappear if you need to if they are far away. It is VERY easy to get smoked by minibosses.
For world 4’s boss, it’s especially important to get rid of the underlings quickly, keep leaf protection with you, and keep the boss away from the gate, because it will shock you and paralyze you for a good 6 seconds at a time. If you get paralyzed while you are not defending the gate adequately, then you’ll be overrun very quickly and there will be nothing you can do. Use all four power ups at once here to destroy the underlings quickly as soon as the boss round begins.
At the very bottom of the upgrade screen between rounds are permanent upgrades. These cost a LOT of gems to buy, so you’ll pretty much have to purchase gems or spend forever grinding for free ones, but the upgrades will have permanent effects that last for every round that you play in Tap Quest afterwards.