This is very beautiful Song, I have found it while reading "THE SPIRITUAL HERITAGE OF TYAGARAJA" (E-BOOK link) and bookmarked in order to find the original Lyrics later.
The following Lyrics and translation from http://sahityam.net/wiki/Amba_Nilayatakshi
ambā nīlāyatākṣi karuṇā kaṭākṣi
akhila lōka sākṣi kaṭākṣi
Oh Mother Neelayatakshi, the Goddess with blue eyes, show mercy, The one who bears witness to the entire universe, show grace.
Anupallavi
bimbādhari citprati-bimbā dhari
bindu nāda vaśaṅkari śaṅkari
(madhyama kāla sāhityam)
ambujā ramaṇa sōdari ati rathi
ambari kādambari nīlāmbari
The One whose lips are sweet and red like the bimbA fruit, bears the reflection of consciousness.
The One who absorbs the sounds of the subtle emanations of the nada bindu, the ever-auspicious.
The Sister of The Husband of Lakshmi, the expert charioteer.
The one who pervades the realm of space, wears the Kadamba flowers and wears blue silk.
Charanam
śiva rājadhānī kṣētra vāsini śrita jana viśvāsini
śiva kāyārōhaṇēśōllāsini4 cidrūpa vilāsini
nava yōgini cakra vikāsini nava rasa dara hāsini
suvarṇa-maya vigraha prakāśini suvarṇa-maya hāsini
(madhyama kāla sāhityam)
bhuvanōdaya sthiti laya vinōdini
bhuvanēśvari kṣipra prasādini
nava māṇikya vallakī vādini
bhava guru guha vēdini sammōdini
