Username: kitttykatz
Played melee all through the first playthrough. Melee Athena starts to get fun when you get to Rend, and then is super fun when you get to Blood Rush.
Skills - At the end of Normal mode, my skill tree looked something like this.
As I progressed toward 50, I continued in this order: Hold the Line > Prismatic Aegis > Clear > Vanguard > Return Fire (or Invictus, if you prefer or have a Relic that fits) > Wrath of the Goddess.
I'd advise putting a point into Maelstrom before you do anything else. Almost all enemies in the core game are weak to shock and/or fire, so you might as well get bonuses from using those elements. Really helps later in the game.
None of the shield regen skills. You want your melee shield down at all times.
If a skill is primarily about increasing gun damage, I don't use it while I'm in full-on melee mode.
I don't know/care if You've Got Blood On You does much damage. I put one point in for the stun effect and because it's cathartic to watch enemies explode.
Some enemies aren't easy to melee. It's just how they're built. It's worth re-speccing to the other skill trees when it's time to fight these enemies. In such situations I usually keep Gun Kata, Omega Senshu (maybe her best skill) and sometimes Rend, and put the rest of my points elsewhere. Not saying you can't do it... but it'll be easier and more fun to use some guns.
You won't always have a strong enough melee shield to really be effective as a melee-only character. During those times, I tended to re-spec a bit to the skills that also increased gun damage, such as Gun Kata, Tear, or any skills in the first two levels of the right skill tree.
Gear
Guns: You REALLY need at least one bladed weapon (shotguns, pistols, SMGs are best) and a quality melee shield. Long delay and high damage.
'Nades: I didn't worry about stripping the shield and instead preferred health regen grenades, but maybe that's just me. Shock or ice.
Freezing enemies massively increases melee damage, so ice gear is great. If you use maelstrom, shock and fire weapons will also up those stacks quickly.
Oz: Melee bonus, health regen or speed boost kits. Ice or shock if I could get them. Didn't really care about damage so, for example, I kept that first Springs Oz kit (level 3) through the entire mode and used it's health regen whenever I was out of atmosphere.
Relic: Blue or up, boosts to 1) Omega Senshu, 2) Whatever else you want. Omega Senshu is huge.
Playstyle
Shoot enemy. Action skill. Melee enemy. Move on to next enemy and melee. Continue until no other nearby enemies, then try to kill whatever is not being killed by Rend. If your melee shield is down, you're probably killing stuff pretty easily. If not, try to keep every enemy in front of you and you'll be ok.
When action skill runs out, retreat and rely on guns. Use grenades and Bloodlust to keep health up.
Rinse, repeat.
Jump a lot before you have Blood Rush and/or when getting mobbed, or when you have an Oz kit that gives bonuses to aerial melee.
My Thinking
Pretty simple: Maximize the health regen, damage and stun bonuses from slashing an enemy. Once I have Blood Rush and Mercurial, I also want to use my speed and mobility bonuses to zip around everywhere, making it tougher for enemies to hit me.
I'm nigh invincible with my action skill up but, because I generally want my shield down, I'm pretty well defenseless with no action skill or shield. Plus, when my skill is up, I can cover a lot of ground quickly. Hence the exaggerated attack/retreat approach.