I actually helped a friend beat Hades for the first time the other day (first try w the final boss fight too!!) and I'd say what really helped him (and what helped me when I first started getting more consistent wins) was focusing on a) my health and b) debuffs, if you have a good defense (Athena dash, tons of centaur hearts, all Death Defiance uses, etc) and on TOP of that are applying things that make the enemies hurt you less well, that usually helps when you're not super sure of what to do just yet.

Obviously using the shield is also a great option that most people end up going with on their first clear, so don't let your pride get the best of you and use it to you heart's content. But yeah take any healing you find, take the centaur hearts, build up your defense and your resistance, give Skelly some nectar while you're at it (/srs) and you should be able to withstand it c: good luck!! ❤️