Choosing a path
After finishing the tutorial forest the real game begins. You can choose between starting at any of the 4 elemental forests.
Each of the 4 levels are about the same difficulty and experience payout. For example the Divine Beasts found in Water Shade are the same level as those in Firewalking (both are the 3rd level of their element). The only real difference is their element, species, and the layout of the map. Because of this it is highly suggested that you advance through the forests in waves: as in finish all of the first sections before completing the second sections. If you do this your team of Divine Beasts will remain at a nice level advantage to help you be prepared to defeat the boss at the end of each forest.
You will have to finish every level of each elemental forest to advance to the next plot development.
Advice for starting out
While your first 2 Divine Beasts are still levels 1-5 they are incredibly fragile. Your first few trips into the forest should be to get your first few levels and perhaps some nice items to help you along the way. Since you still have not gotten too deep into the forest having to backtrack is actually a benefit so return to the temple any time your team is looking vulnerable to a defeat and then go back to the forest you were working on exploring. This will heal your Divine Beasts for free and fighting a few extra battles is good experience. If this is not your style then stop by Kikinack and Co. before going to the forest and stocking up on healing items instead.
Be sure to also keep track of the Bulletin board for jobs. Take any that look appealing or you think you can finish in a timely manner (if you take too long finishing a job you will still get the reward but will not get any additional reputation). When you have accumulated enough reputation visit the arena and participate in tournaments to increase your rank. When your rank increases you can keep an additional Divine Beast on your BeastAmulet and an extra shield. This supplies you with an immense benefit so always strive for the highest level you can obtain. The standard ways to earn reputation is finishing jobs and turning in Kalma to the Room of Life.
Overview of the elemental forests
To advance to the next major plot development you must collect the orbs in each forest. These legendary orbs are guarded by the final boss at the end of the 4th forest in each elemental grouping. Each element has its own individual story arc and set of NPCs. Along your journey you will find many new allies and enemies that will either help or hinder you.
Facing each forest should be good practice on learning how to counter and defeat the different types of Divine Beasts by element. If you are having difficulties getting through a specific element then it may be a sign that you should try an alternate tactic or alter your BeastAmulet's team.