The story of glory

No sword, no arrow, no club in my hand,
But strength of sheer muscle foretold the beast's end.

I called upon rocks to bury it dead.

The goddess felt so lonely I had to spend a year,
To capture gold and bronze on top of wounded deer.

A huge a fearless beast was trapped in a snow mound,
I caught it in my net, oh, great was my reward.

A man just got my help to clean all of his mess,
But I did gain just nought, though river I posessed.

The iron birds afly, my arrows turned them down,
A rattle as reward, they ran not to be found.

Fire in its eyes, pouring from its nose,
Throttled with bare hands, fear me, who oppose.

Eating human flesh is a monstrous thing,
Fight fire with fire, devoured was the king.

The women who fight not less than the men,
Had belt I desired so fought for it then.

Three heads or three bodies are not enough for me,
I could kill a star, so god rewarded me.

The gold, the ladies, the dragon-like guardian,
The trick, the apples, the enormous burden.

A puppy you'd call it, too many is three,

Replace the owner's or place's sole head
With one that is half of the journey ahead.

Agrnudgh is my name, just know my full story
Of pain and the labour and strength and the glory.

What/who am I?

The last two stanzas explain the name Agrnudgh used there. (notice the "cipher" tag)

• Too much of a labour for me this one... – Brent Hackers Feb 2 '17 at 8:48
• Yeah, solving this puzzle would be a Herculean task. I'm not sure I could do it. – Deusovi Feb 2 '17 at 8:52
• Hmmm... Could the hint be to do with one of the similar but different stories from mythology? eg. the epic of Gilgamesh, or Beowulf, or The odyssey? Or is it something still related to the more obvious subject of the other stanzas? – Brent Hackers Feb 2 '17 at 9:30
• @BrentHackers If it is about another story, then there must be some clue about which one it is. If there is no such clue, then it is all the same story. – oleslaw Feb 2 '17 at 9:34
• Oh... Just noticed the cipher tag and my brain went into stand-by mode. – Brent Hackers Feb 2 '17 at 9:41

I think I figured out the last two stanzas.

Replace the owner's or place's sole head

The "sole head" refers to the first letter of the owner or place in the name of the labors:

Nemean Lion
Lernean Hydra
Hind of Ceryneia
Erymanthean Boar
Augean Stables
Stymphalian Birds
Cretan Bull
Horses of Diomedes
The Belt of Hippolyte
Geryon's Cattle
The Apples of the Hesperides

So that gives us NLCEASCDHGHH as our key.

With one that is half of the journey ahead.

"Replace... With..." suggests a substitution cipher.
"Half the journey ahead" is literal, so the first letter gets replaced with the 7th in the key:

NLCEASCDHGHH
↓↓↓↓↓↓↓↓↓↓↓↓
CDHGHHNLCEAS

Every letter not in the key is unaltered.

Agrnudgh is my name, just know my full story Of pain and the labour and strength and the glory.

So using the substitution we've found:

AGRNUDGH
↓↓↓↓↓↓↓↓
HERCULES

So as we suspected from the story, you are

Hercules!

• That's exactly why the cipher tag is there. – oleslaw Feb 2 '17 at 14:02
• Some day I will learn how to do this stuff.... Some day. +1 Sabre – Brent Hackers Feb 2 '17 at 14:59

Oh, what the heck...

You are Hercules and you're describing the labours?

No sword, no arrow, no club in my hand, But strength of sheer muscle foretold the beast's end.

First Labour: Nemean Lion

Second Labour: Lernaean Hydra

The goddess felt so lonely I had to spend a year, To capture gold and bronze on top of wounded deer.

Third Labour: Ceryneian Hind

A huge a fearless beast was trapped in a snow mound, I caught it in my net, oh, great was my reward.

Fourth Labour: Erymanthian Boar

A man just got my help to clean all of his mess, But I did gain just nought, though river I posessed.

Fifth Labour: Augean Stables

The iron birds afly, my arrows turned them down, A rattle as reward, they ran not to be found.

Sixth Labour: Stymphalian Birds

Fire in its eyes, pouring from its nose, Throttled with bare hands, fear me, who oppose.

Seventh Labour: Cretan Bull

Eating human flesh is a monstrous thing, Fight fire with fire, devoured was the king.

Eighth Labour: Mares of Diomedes

The women who fight not less than the men, Had belt I desired so fought for it then.

Ninth Labour: Belt of Hippolyta

Three heads or three bodies are not enough for me, I could kill a star, so god rewarded me.

Tenth Labour: Cattle of Geryon

The gold, the ladies, the dragon-like guardian, The trick, the apples, the enormous burden.

Eleventh Labour: Apples of the Hesperides

A puppy you'd call it, too many is three, I leashed it from under to surface for free.

Twelfth Labour: Cerberus

Replace the owner's or place's sole head With one that is half of the journey ahead.

Agrnudgh is my name, just know my full story Of pain and the labour and strength and the glory.

Jason and the Argonauts

• Almost, but the last stanza is not about Jason. – oleslaw Feb 2 '17 at 8:59

Hercules

No sword, no arrow, no club in my hand,
But strength of sheer muscle foretold the beast's end.

Hercules killed the snakes sent by Hera when he was a baby by strength alone.

I called upon rocks to bury it dead.

He killed the Hydra.

The goddess felt so lonely I had to spend a year,
To capture gold and bronze on top of wounded deer.

during his labors he had to get the deer of Artemis, which was either silver or gold, don't remember.

A huge a fearless beast was trapped in a snow mound,
I caught it in my net, oh, great was my reward.

he had to bring the Erymanthian Boar, which he trapped in snow.

A man just got my help to clean all of his mess,
But I did gain just nought, though river I possessed.

he cleaned the poop from Geryon's stables using a river that he diverted, but Geryon betrayed his trust.

The iron birds afly, my arrows turned them down,
A rattle as reward, they ran not to be found.

the Stymphalian birds, he shot them with arrows.

Fire in its eyes, pouring from its nose,
Throttled with bare hands, fear me, who oppose.

Eating human flesh is a monstrous thing,
Fight fire with fire, devoured was the king.

The flesh eating horses, Hercules fed Diomedes to his own horses.

The women who fight not less than the men,
Had belt I desired so fought for it then.

Hi-whatever's belt, of the Amazons

Three heads or three bodies are not enough for me,
I could kill a star, so god rewarded me.

??

The gold, the ladies, the dragon-like guardian,
The trick, the apples, the enormous burden.

Ladon and the garden of the Hesperides

A puppy you'd call it, too many is three,