Tip 1
The most important thing is to explore the map as much as possible until you have no other places to go and only then start attacking the monsters. This way, you collect all materials that are required to help you easily defeat them.

Tip 2
Remember what each thing on the map will give you. For example, there are items that increase your health as soon as you tap that hexagon (such as the fish) and if you have maximum health, you basically waste a great free health refill. Always know the potential effect of the items in each hexagon.

Tip 3
Don't hurry to craft things and only do so when really needed. Materials are scarce and you can still collect items along the way. Since items share materials required for crafting, this micromanagement thing can help you get a long way.

Tip 4
There is no need to defeat all monsters in an area. There might be a requirement to defeat all the monsters of a particular kind, but if there's none, you can just move on without attacking. Of course, it's up for you to decide if you should do it or not.

Tip 5
Monsters usually guard important items that can help you move forward. The monsters themselves can sometimes give you some sort of a boost or item, so always make sure that you make the right decision, carefully weighting risks and rewards. If monsters are easy to beat, always defeat them all to increase your rewards. If the mission is tough, do some planning and only destroy those who really matter.

Tip 6
Boost your stats when needed using the items in your inventory or by crafting items. They all have limited uses, so make sure that you equip a sword for example when you really need the attack boost - you can't unequip an item and after equipping it!