The first one is a projectile that is randomly shot from any of his segments. This does 75 damage.
The second attack is when he lays down damaging rocks, much like the Rock Scarab. These deal 99 damage.
The third and most used attack is when he lunges at you, attempting to come into contact with you. Contact with the body or tail of Mykonogre results in you being dealt 99 damage, so watch out. His tail can also hit you for contact damage.
He has a ton of health, but makes up for this by having multiple segments. This allows you to use a piercing weapon for a lot of DPS. It is recommended to have a team of 2-5 people with good piercing weapons, as it will take a while to take him down due to his massive health pool.
Like stated above, take a team of 2-5 people and make sure at least one of them has bubble with a good amount of faith. Every person should bring piercing weapons to the fight. War-forged gun is especially good for this boss because the turrets pierce through the multiple segments and do a lot of damage. Using hyperbeam while the boss is lined up horizontally with a good amount of DEX can do tons of damage and help a lot in killing the boss. Try using your piercing weapon when he is lined up horizontally, so your shots can hit all his segments. Recommended mods are Crit dmg, Crit rate, and Projectile range. The crit mods can help to do a lot more damage, and the projectile range helps piercing weapons hit every segment of the boss.
He has a chance to drop Mykonogre H or Mykonogre A on death, which are both very good armor pieces for strength-based cadets.