Myrlwood Forest, similarly to Malmalan Thicket, is quite a linear location where you won't be able to get lost - you will be following the only available path during the whole time. There are only three types of enemies here and numerous valuable items hidden inside. Additionally, the place holds the Royal Tomb, with the immensely powerful Start of the Rogue weapon inside - one of the best weapons in the game. The recommended level for this location is 35.
Myrlwood Forest is located in the north-western part of the map, right next to The Vesterpool. The easiest way to reach it is to use Regalia and go to The Vesterpool parking spot and cover the rest of the distance with a Chocobo. The exact location can be found on the above screenshot.
Vulnerable to Swords, Firearms and Fire, resistant to Lightning and Light. Inflicts Mollified (reduces Strength) and Confused statuses.
Vulnerable to Polearms, Shields and Ice, resistant to Fire and Ice. Can poison ("Poison" status).
Vulnerable to Greatswords, Machinery and Fire, resistant to Lightning and Light.
Like in most dungeons, the enemies found in Myrlwood Forest are resistant to weapons infused with the Light element. The most effective weapon type to use against the boss is definitely a Greatsword, and the whole encounter can be made even easier by using Ignis' Enchantment ability, allowing you to deal additional fire damage.
Run through a narrow passage between rocks to get inside Myrlwood Forest. After a short walk you should stumble upon the first enemy in the area - Mushussu. The enemy isn't anything special - it won't deal any significant damage and its poisonous attack, even though it causes the Poison effect, can easily be neutralized with Antidotes. Polearms are effective against those foes, although Greatswords will be even better - two-three strikes with the two-handed swords are more than enough to eliminate them.
Once you're done, continue your march and you should encounter another group of enemies, consisting of Mandrakes and a Mushussu. The enemy isn't that strong, but it can inflict two negative statuses. The first one, Mollified, decreases the Strength attribute of a character, whereas the second one is "Confused". With the latter your controls will be reversed and your companions will sometimes miss their attacks, slashing through the air. Mandrakes are quite slow, which should allow you to take at least one of them out before they can do anything - take advantage of their weakness to Swords. However, you should focus all your attention on Mushussu and then take out the Mandrakes. There will be another Mushussu wandering around the area (to the north of your current position) - go there, take it out and continue going west.
The group should soon encounter a pair of Mandrakes - take them out and continue travelling west, leading you into a narrow passage with two Mushussu blocking the way. Eliminate them, continue the march and take out a group of three Mandrakes. You should now be at a fork - the route to the south leads to a fishing spot, a place to set up a camp and all three elemental deposits. Go there to rest, fish at the fishing spot and get back to the form, from where you have to head west.
At the end of a narrow passage you will be "greeted" with a pair of Mushussu. Take them out and continue traveling west, until you reach an open area. The last enemy of the dungeon - Treant - awaits you here. The foe is vulnerable to Greatswords and the damage output against it can be increased even more by using Ignis' Enhancement ability, giving your attacks extra fire damage. The enemy can hit pretty hard, although its attacks are easy to dodge and/or parry. If you have any problems with the boss, wait for the parry prompt to appear on the screen and focus on counterattacking. The enemy can be easily weakened (and you can gain an extra item from it) by focusing attacks on its head - several strikes should be enough to cut the horn-like branch off its head.
Once the encounter is over, head to the nearby Royal Tomb to acquire the immensely powerful Star of the Rogue weapon. The dungeon is clear, you've collected the weapon and you can leave the area.