Elysium is the third region of the game. Beating Elysium entails navigating your way through several different rooms. Not all of which are guaranteed to contain encounters in which you fight enemies.
Some general tips for the encounters:
The enemies that look like warriors and hold swords, bows, shields, etc. will turn into floating orb-like creatures when you will them. You must kill these as well. If you do not, they will turn back into their human form and you will have to kill them again.
If you see the wheel with the three choices, this lets you meet Patroclus. Patroclus has some VERY good buffs to give you that can help you with the bosses of Elysium and perhaps the final boss too. The most noteworthy is the ability to completely refill your Death Defiance mirror perk.
The minibosses in this region are not easy at all especially if you have not beaten Elysium yet. The two minibosses are a giant Soul Catcher (butterfly ball) and Asterius, the Minotaur. If you are against the butterfly ball, kill the butterfly ball as soon as possible. Enemies will continue to spawn infinitely until the butterfly ball is dead. Asterius is a little easier in my opinion. He jumps around a lot and will charge around even more. As soon as you see him coming your way, dash out of the way and then hit him. To give yourself more time to hit him, dodge while he is charging towards a wall or pillar and he will be stopped for a second.
At the end of Elysium, you will face a duo boss: Theseus and the Minotaur (Asterius). If you beat Asterius as a miniboss, he will start the fight with less health.
This fight is not easy and will require some patience and practice to get this down. Asterius behaves the same way that he did during the miniboss fight. Theseus, however, is very annoying. He will throw spears at you and will do damage when he pulls it back. When you see the pink marker on you, dodge to behind a pillar. Theseus will also hold his shield in front of him making him impervious from the front and you must attack him from the back.
When either of them gets to half health, they will behave differently. Asterius will become more aggressive and charge more. Theseus will call upon a god and spam the field with damaging areas. Do NOT get Theseus down to half health until you have beaten Asterius first. You will be dodging a lot during this fight.
Choosing the right weapon to fight with purely comes down to your own personal preference. The shield is a safe weapon, the Aspect of Chaos is especially good if you want to play defensive and special your opponents to death. Experiment around with what works best for you, but overall the fight can be done with whatever weapon. If you want to upgrade a given weapon, spend Titan's blood that your earn by beating Meg with the various weapons. I don't recommend selling the Titan's blood until you have beaten the final boss.