Menace Beneath Lucis is a post-game side quest which you will have after talking to Ezma, an old lady who will also give you the Sealbreaker's Key. According to Final Fantasy XV lore, no one has defeated the monsters yet and it's your team's turn to try and defeat them to bring Lucis to complete peace. Here are some tips how to defeat the eight final bosses.
A Giant Flan
This will be the only enemy you will encounter in Keycatrich Trench. Although it is an over-sized Flan, it is no different from variants of its kind except that it has more health than the normal ones. Defeat it by just steadily dealing damage to it until it dies. Also note that in order to defeat it with ease, you need to be a Level 55.
Kenga
This will be the final boss fight in the Menace Under the Grotto which takes place in the Greyshire Glacial Grotto. The Kaenga uses similar attacks just like the samurai daemons in the game except that it has more health. You can defeat it by using the same technique you used in defeating the samurai daemons, such as the Ronin.
Chandravarma
This is a powered up version of the Red Giant and is the final boss at Fociaugh Hollow. Be careful of its shockwave when it launches a ground pound attack and an orb that pulls and damages your team. It also has some sweeping sword attacks which you need to be careful of. Also take note that it is immune to all your attacks except your Armiger. Use the same technique like you would when you face any Red Giant.
Mahanaga
The final boss in the Daurell Caverns, the Mahanaga is similar to the Naraginis, a snake-like daemon. It has the power to transform you into a toad using is poisonous train. Its weakness is lightning and swords. Once you defeated it, you'll get the Enhancer sword.
Pyromancer
The Pyromancer is the final boss in Balouve Mines. It will use two types of attacks against you - a blue-triangle beam that will petrify you and a poisonous breath attack that can instantly kill you if you are not fast enough to dodge it. It also has a grab attack which can cause you damage until you loosen yourself from its grip. Kill it like you would any Pyromancer and you'll get the strongest weapon in the game - the Death Penalty.
Wyverns
You will encounter these powerful beasts at Steyliff Grove. You can render damage to and finally defeat them by using most of the weapons you have. Once you defeated them, you'll acquire the Aegis Shield. Take note that this side quest might take longer than the others. Also, you have to enter Steyliff Grove at night - between 7 PM and 4 AM.
Jormungrand
This is the final boss battle in Crestholm Channels. Always keep in mind to stay at a distance and be aware when it starts to curl up because it build up a fire attack inside it which can instantly kill you and your team if you are within range. It is weak against Blizzard attacks so use them to weaken the monster.
Jabberwock
This is a pretty straightforward fight in Final Fantasy XV where you have to use plenty of Blizzard spells. Don't forget to bring a lot of items with immunity because the Jabberwock has a lethal petrify attack.