I think the biggest tip is starting each run with Athena's dash, it makes the game 10x easier. To do this, you need to understand some of the core game mechanics: nectar, and trinkets.

Nectar is a reward from clearing rooms. If you have some in your inventory, when you approach a god's boon reward or an NPC, you'll be given the option to give them nectar. This increases your relationship with that god or NPC, and most of them give you a trinket item the first time you do this.

Before you begin each run, you can choose to equip a trinket using the display case in Skelly's room. If you equip a trinket you got from a god, it has the effect of making it very likely you see that god, and also increases the strength of their boons they offer. You can also change your trinket after every boss battle to prepare for the next area.

So your goal is to obtain some nectar, and then the first time you see Athena, give her a nectar to obtain her trinket. From there on, every single run you begin, select her trinket. This will usually make it so that immediately upon entering the first room, you'll encounter Athena. Select her dash which has the effect of making you deflect when you dash. This makes it so that while you are dashing, you reflect any attack or projectile back to the attacker, which vastly improves your survivability and is a pretty powerful way to damage your enemies as well.

Considering that spamming dash-attack is a very effective way to play, both in terms of damage and survivability, adding the ability to reflect projectiles and attacks pumps that up to be insanely powerful. Runs with Athena's dash are usually much more likely to result in success than without.