Short answers, pulled from the story.
Penthesilea was an Amazonian queen, the daughter of Ares and the sister of Hippolyta, Antiope, and Melanippe. She led Amazon warriors to fight for Troy in the Trojan War and was killed by Achilles. The asteroid 271 Penthesilea, discovered in 1887, was named in her honor.
The Aethiopis is a 5-book epic attributed to Arctinus of Miletus, published in the 8th century BC and part of the Epic Cycle of poems about the Trojan War. It describes Penthesilea as a Thracian woman warrior who arrives at Troy with twelve Amazon companions. Achilles kills her, and when the soldier Thersites mocks him for falling in love with her, Achilles strikes Thersites dead.
Medieval writers replaced her ancient military motive with a romantic one: love for the Trojan hero Hector. Benoît de Sainte-Maure's Roman de Troie, written in 1160, established her as a chivalric heroine who knelt before Hector's corpse and vowed to avenge him. Christine de Pizan featured her in The Book of the City of Ladies in 1405, and Giovanni Boccaccio devoted a chapter to her in De Mulieribus Claris, completed between 1361-1362.
In Kleist's drama, structured in twenty-four consecutive scenes, Penthesilea kills Achilles rather than being killed by him. She and her dogs maul him, and when she understands what she has done, she dies through what Kleist calls "a crushing feeling." The drama was the basis for Othmar Schoeck's 90-minute one-act opera, which premiered in Dresden in 1927, and for Pascal Dusapin's opera, which premiered in 2015 at La Monnaie in Brussels.
The Bassae Frieze at the Temple of Apollo Epicurius, built in the mid to late 5th century BC, shows Achilles killing Penthesilea on the slab known as BM 537, where she is identified as a queen by a crown. The Penthesilea Painter, an Athenian artist active between 470-450 BC, depicted her so frequently that art historian Adolf Furtwangler named him after her. Pausanias also recorded a painting by Panaenus on the throne of Zeus at Olympia showing Achilles supporting the dying Penthesilea.
Quintus Smyrnaeus, a Greek poet of the 4th century AD, opened his Posthomerica with Penthesilea's story, giving the legend an origin not found in earlier sources. He describes her as having accidentally killed Hippolyta with a spear while hunting deer, leaving her to seek an honorable death in battle. In his account she kills eight Greek warriors and inspires the Trojan women to fight through the speech of Antimachus's daughter Tisiphone.