Tragedy in Three Acts

Here are the flavor texts of each one of the six artifacts required for this achievement. For quick reference. As well as to make it easier for readers to figure out the story of Pyramond and Theleste.

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• This box is of sandalwood with a tiny clockwork elf and nightsaber within. Although the winding mechanism is no longer functional, you can imagine the two would dance together while music played. Engraved on the bottom: 'To my dearest Theleste.'

  
  Not a terrible lot one can extract from this one. Pyramond loved Theleste and gave her this music box as a gift.
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• This clasp is fashioned of lacquered wood carved to resemble stag antlers. On the reverse is engraved the name 'Pyramond' in Darnassian.

  
  So Pyramond owned this. One could claim the antlers were some symbol associated with him - perhaps he was a druid? Or a noble?
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• Engraved beneath the setting for the precious stone are the words 'To Theleste, on her twenty-fourth birth year.'

  
  Another one of Pyramond's gifts, likely. It could be from her parents, but the precious stone makes that option seem unlikely. Also, the fact that this was a gift for Theleste's 24th birthday suggests that she was probably not an elf - she would have been to young for romance at that age. Human, maybe? We don't know how old the artifacts are, but if they were from the pre-Sundering times, that would be almost impossible, as night elves and humans did not interact. Could be an elf, after all...
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• Remarkably, you managed to find an entire menagerie of these elven glass animals in their original storage container. While some of the animals have understandably suffered cracks and chips, it is clear that the head of the stag has been deliberately severed. The initial 'T' is carved on the bottom of the chest.

  
  This one is puzzling. It looks like the chest belonged to Teleste, as indicated by the initial 'T'. The head of the stag being deliberately severed vaguely suggests strong negative emotion - hatred or sadness/despair. Since we know the chest is related to the story between her and Pyramond, we could assume that the stag is another symbol for Pyramond - after all his cloak pin had antlers on it. Both noble and a druid are equally likely vocations for Pyramond.
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• A note in rich vellum is tied to the bottle. 'Dearest P, now that I know we can never be together, it is my wish to drink this draught of spider venom. If this note finds you, my hope is that you might do the same. May Elune watch over our souls.'

  
  The "dearest P" must be Pyramond. For some reason Theleste decided that the two can't be together and pulled a Juliet on him. Her call to Elune suggests that either she was an elf, or her love for Pyramond made her believe in the moon goddess.
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• While this elven scroll case is graced with much ornamentation, it is the message inside, written in Darnassian, that is of the most interest: 'Pyramond, under no circumstances are you to spend time with that tavern wench. Your mother and I forbid it. She is far beneath your station.'

  
  This must be from Pyramond's father. The language of choice suggests that they were all elves, and there is a likelihood that Pyramond's family was noble as well. I can't imagine an elf being a "tavern wench", but apparently Theleste was considered one by Pyramond's parents. Maybe she was a human after all?
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There are many holes in the story, but it looks like Pyramond was a young noble, perhaps the heir in his house. His family's crest was a stag - or antlers, at least. At some point of time he fell in love with Teleste - a human or an elf girl; young, perhaps working as a waitress in a tavern - or whatever equivalent they had at the time. The two loved each other, but Pyramond's parents found out about the relationship and forbid their son to see his love. Theleste learned that somehow, could overcome the pain, and drank a vial of spider poison, ending her life. She left a note for Pyramond, asking him to do the same so that they could be together in the afterlife. Sometime before she committed the suicide, she - in a fit of sadness or rage - ripped the head off the glass stag, presumably given to her by Pyramond.

All six of the artifacts are common tier items from the Night Elf tier in archaeology.

Cloak Clasp with Antlers
Hairpin of Silver and Malachite
Delicate Music Box
Chest of Tiny Glass Animals
Cracked Crystal Vial
Silver Scroll Case

The achievement's name is likely a reference to three-act plays as a general subject.

The names "Pyramond and Theleste" are likely references to Pyramus and Thisbe, two characters from Ovid's Metamorphoses, in a story very similar to most romantic tragedies, that has been noted to be the source of Shakespeare's more widely known Romeo and Juliet.

Indeed, the items necessary for the achievement do reference these dramas, as well as others.

The Cloak Clasp with Antlers is a reference to Pyramus and Thisbe itself, as Pyramus sees Thisbe's cloak on the ground, torn to shreds by the nearby lion, and mistakenly interprets it as a sign of her death.

The Cracked Crystal Vial is a reference to Romeo and Juliet, specifically the vial of poison that Romeo purchased from an Apothecary for the purpose of suicide should he find Juliet dead.

The Hairpin of Silver and Malachite is a reference to the Chinese folktale of Niu Lang and Zhi Nu. The Hairpin in the tale was one of gold, and it was used by the Queen Mother to make a large river appear between the lovers.

The Chest of Tiny Glass Animals is a reference to The Glass Menagerie, a memory play. The glass animals are prized possessions of Laura, one of the four major players in the drama.

The Delicate Music Box is hard to place as a reference; it is likely not a reference to a specific work, but rather to the general romantic nature of Music Boxes.

The Silver Scroll Case is much harder to place. I have found no likely reference as of writing.