Asteria was the daughter of Danaus and either Atlanteia or Phoibe (both Hamadryad nymphs of Libya in north Africa as well as wives of King Danaus). Asteria would be one of the Daniads who murdered her husband (Khaetos) following the mass marriage of the daughters of Danaus to the sons of Aigyptos.
When Asteria and the other Danaids who had murdered their husbands they were sent to Tartarus and were forced to carry water from the river Styx in a bowls (or jars according to some) with holes over to a tub which leaks at multiple parts. Asteria and the others were told only when they filled the tub could they wash away their sins. The Danaids continue this essentially impossible task to this very day.
Danaus & Atlanteia or Phoibe
"[The daughters of Danaus married the sons of Aigyptos:] Hippodameia went to Istros, Rhodia to Khalkodon, Kleopatra to Agenor, Asteria to Khaetos, Phylodameia to Diokorystos, Glauke to Alkes, HippoMedusa to Alkmenor, Gorge to hippothous, IphiMedusa to Eukhenor, and Rhode to Hippolytos. These ten sons had an Arabian mother, while the girls were the daughters variously of Atlanteia and Phoibe, two Hamadryas Nymphai."
- Pseudo-Apollodorus, Bibliotheca 2. 17 (trans. Aldrich) (Greek mythographer C2nd A.D.)