अन्वयः

अनर्थरूपा misfortune incarnate, सिद्धार्था with her purpose fulfilled, अङ्गना that woman, अतदर्हम् who did not merit such treatment, अतथोचितम् who was not accustomed to that (treatment), पुण्यान्ते after exhausting the merits (earned), देवलोकात् from the heaven, परिच्युतम् fallen, ययातिमिव like Yayati, शयानम् lying, महाराजम् to the maharaja (Dasaratha), अभीता fearless, भयदर्शिनी displaying fear, पुनः again, तमेव वरम् those very boons, आकारयामास urged.

M N Dutt

Then as the mighty king was lying down in this unbeseeming and improper guise, like Yayāti dropped from the celestial, that lady, personating the ruin of the race, not fearing public odium, who had discerned danger from Rāma to Bharata, not having attained her wish, again addressed the monarch, concerning the boon he had promised to her.

Summary

The maharaja lying on the floor resembled (king) Yayati fallen from heaven after his merits (earned earlier) were exhausted. He neither deserved nor was accustomed to such (humiliating) treatment. Fearless Kaikeyi ,the incarnate of misfortune having accomplished her purpose, displyaing feigned fear, urged the king again (without inhibition), about the boons:

पदच्छेदः

अतदर्हं	अतदर्ह (२.१)
महाराजं	महत्–राज (२.१)
शयानम्	शयान (√शी + शानच्, २.१)
अतथोचितम्	अतथोचित (२.१)
ययातिम्	ययाति (२.१)–ययाति (२.१)
इव	इव (अव्ययः)–इव (अव्ययः)
पुण्यान्ते	पुण्य–अन्त (७.१)–पुण्य–अन्त (७.१)
देवलोकात्	देव–लोक (५.१)–देव–लोक (५.१)
परिच्युतम्	परिच्युत (√परि-च्यु + क्त, २.१)–परिच्युत (√परि-च्यु + क्त, २.१)

छन्दः

अनुष्टुप् [८]

छन्दोविश्लेषणम्

१	२	३	४	५	६	७	८
अ	त	द	र्हं	म	हा	रा	जं
श	या	न	म	त	थो	चि	तम्
य	या	ति	मि	व	पु	ण्या	न्ते
दे	व	लो	का	त्प	रि	च्यु	तम्