Neon Abyss

Ares (the God of Violence) and Athena (the Goddess of Illusion) are both reached in similar ways. You'll first need to beat Zeus, the God of Lightning, at the end of a run before you can reach these two bosses. Refer to Shutdown (20G) for that.

Now that your runs consist of seven floors, you can attempt to reach and fight Ares or Athena. You can only fight one per run, so decide ahead of time which one you want to try for. 

The process for reaching each of these bosses is related entirely to your Faith meter in the lower right corner. In this paragraph, I will explain exactly how Faith works. Your Faith meter can either be red (Violence) or purple (Wisdom). There are certain actions that change the color, and certain ones that just move the meter. For example, the purple crystal chests you find in rooms and the purple doors leading to the shop on each floor are both things that can switch the color of your Faith meter. Additionally, you should get the Crystal Device skill from the skill tree. This shows up in random rooms and also can change the color of your meter. For all three of these things (crystal chest, crystal door, and crystal device), using crystals on them will automatically turn your meter purple, to Wisdom. If your meter is already purple, it'll give you a significant bump in your meter. On the flip side, if you damage the chest, door, or device, it'll turn red with spikes. You now need to touch it to take damage and open it. This automatically turns your meter red (Violence), and likewise gives a significant increase if your meter is already red. The only other way to move your meter is how you perform in combat rooms: if you take no damage, you will get Wisdom, but if you get hit at all, you get Violence. Note though, that the color of your meter won't change from combat performance. If your meter is purple and you beat a room without getting hit, it'll go up. If your meter is purple and you get hit in a room, it'll go DOWN. Likewise, if your meter is already red and you get hit in a room, it'll go up, etc. 

In my opinion, Wisdom is way easier to maintain just because you don't have to worry about taking damage intentionally from chests and doors and devices. Either way, fill the meter with Wisdom or Violence depending on which boss you want to find. Once you fill the meter with either color, you'll get an onscreen message. Head to any teleporter and go to the secret room off to one side of the map. For Athena, there will be two items to choose from, just like an item room. For Ares, you need to permanently sacrifice a heart container (not just take damage, but lose an entire heart container). Only then can you choose an item. In either case, once you pick an item from the shrine, there is a chance that a Token will appear next to them. In my experience, it seems to be a 50-50 shot. If the Token appears, pick it up. If it doesn't, you'll need to continue the process of filling your Faith meter again on another floor. 

Once you get the Athena or Ares Token, you no longer need to worry about your Faith meter at all if you don't want to (but you can continue to max it out to get more items from the shrines). Continue the run like normal, beating Zeus on the seventh floor. With him beaten, enter the portal and you'll be taken to a new eighth floor. Proceed through this floor like any other floor and into the boss door to fight Ares or Athena, depending on which token you got. 

Ares is pretty much entirely a melee boss. He charges back and forth, jumps and tried to smash you, and is generally pretty fast. However, by now you should be pretty decked out with good weapons and items, so keep your distance and this fight will actually be pretty easy. Just be ready to jump over his charges. 

Athena flies around and shoots out all sorts of projectiles. He has crystals that explode projectiles, energy balls that circle her and the shoot out, clones that shoot lasers out, etc. It's a fight with a lot to dodge, but it never really gets that chaotic as long as you stay calm and focused. She moves around the air a lot, so it's important to also keep your fire focused on her, as it's really easy for her to slip away while you're concentrated on dodging stuff.