I know that it’s possible to work with Hercules since he ascended to Godhood but what about other Heros from different lores like Achilles or Arjuna?
Some will say necromancy but can you pray to them as you would pray to say Ancestors and work with them in a way as you would with your Deities?
What would they bring into your life? Achilles could help with leadership, Arjuna can help with tough choices or Chiron can teach medicine (he’s not a Hero but he trained heros so yeah)
Thanks in advance
If the heroes are real yes, but even then if not you can also work with the collective belief formed around them as an archetype as well. Although Hercules was a demigod, his trials allowed him to be made into a full God by his father Zeus.
Hiya OP! You can most certainly work with mythical heroes at least in a necromantic context; after all, another term for elevated ancestors of a group or collective is the “heroic dead”! 
The benefits of doing so would vary within the spectrum of their mythical details.