I think I've found my white whale...
Granted I could have played a lot better on all these games I can't seem to understand her role. Do I splitpush or teamfight? Get blink or aghs first? She also seems to have a strange power curve which is counter intuitive for a snowball hero.
I play her a lot lately and honestly, she can be quite hard to win with but once you snowball, you got like the highest DPS in the game (maybe second to CK or Sven, I don't know) and you kill anybody at an instant.
Some things I do:
1. Don't max Power Shot 1st. That skill is not that good and you are better off getting points in your stun as 1 point in Shackle doesn't suffice. I usually go 4-2-1-1 (1-2-1 by level 3) by level 8. There are some match ups where maxing it is beneficial though like against SF. You drain like 40% of his health pool with a level 4 PS but I'm not sure if it's worth. I don't like the skill at all after playing her quite intensely.
2. Agh's first is the correct choice.
3. Get a bottle regardless of which lane you are in since she has sustain problems
4. Blink is good. Shadowblade as well.
5. Go safe lane or mid because she needs a lot of farm and a lot of levels (Level 16 is very helpful)
6. My item build (slahser does it as well):
Basi - Phase - Agh's - Crystalis - Shadowblade - Daedalus - MKB - Skull Basher - Abyssal
BKB or Linken's if necessarry. BKB will be necessary more often than not honestly but I found playing without it quite helpful in learning to play around spells and disables. But that's up to you. You are a 4k god as well if I'm not mistaken so you should be fine.
Once I get to the point where I have SB, I roam the jungle and kill anyone I find. Preferably their carry. Split pushing works really well too as your ult is on low CD and melts towers. Her team fighting is mediocre and I honestly prefer avoiding them. Rather pick someone off and make space for another core (your mid or your safe laner, depending on which lane you farmed) or force a Rosh or an advantageous 4v5 push etc.
But yeah, the fact that she's so ressource hungry and not that useful early game makes her not easy to win with. I think she's good but I regard her as a mid to late, if not late game core. She scales insanely well with farm and levels so don't underestimate farming.