mAnAtIta-prathita-vibhavAM ma~NgalaM ma~NgalAnAM
        vakShaHpIThIM madhu-vijayino bhUShayantIM svakAntyA
    pratyakShAnushravika-mahima-prArthinInAM prajAnAM
        shreyomUrtiM shriyam asharaNastvAM sharaNyAM prapadye

(I), who have no other shelter, salute and worship Shri Devi, who 
* is well known and is exalted beyond all exaltations;
* has taken Vishnu's chest as Her seat, and adorns and decorates it with
  Her beauty; (Vishnu is referred to as the Conqueror of the demon, Madhu)
* is verily the embodiment of all that is good for those who desire to 
  (pray for) excel(ling) in the material or spiritual realm;
==
mAna = respect, honour
atIta = surpassing, exceeding, boundless
prathita = celebrated, renowned
vibhavAm = exalted position, riches, prowess
ma~NgalAnAm = of all auspicious things 
ma~Ngalam = auspicious
madhu-vijayI = Conqueror of the demon Madhu, madhu-vijayinaH = of Him 
vakShaH = chest
vakShaHpIThIm = His chest treated as a seat (Her seat)
kAntiH = lustre, brilliance, beauty; svakAntyA = by One's own splendour 
bhUShayantIm = She, who adorns, decorates
pratyakSha = perceptible, sense-congnizable things
anushravika = relating to sacred traditions, Shastras, spiritual things
mahima = glorious things
prArthinI = one who requests, desires for; prArthinInAm = of such people 
prajAH = subjects, people, mankind; prajAnAm = of them
shreyaH = most excellent, desirable, auspicious, blissful
shreyo-mUrtim = embodiment of all prosperity, auspiciousness
shrIH = Shri Devi; shriyam - subjective form
sharaNyAm = One who is fit to protect, worth surrendering to
tvAm = You (subjective form)
asharaNaH = one who is forlorn, helpless, has no recourse (the poet here)
prapadye = (I) worship, seek (Her) refuge
==
[man, 1 P, manati, 10 A, mAnayate, to be proud, 4, 8 A, manyate, to honour, 
 respect; agree; understand; think]
[i, 2 P, eti, to go towards; arrive at, obtain; arise; atyeti = to go beyond]
[prath, 1 A, 10 U, prathate, prathayati/te, to increase, spread abroad, publish]
[bhU, 1 P, bhavati, exists; happens; vibhavati = to appear, become manifest]
[ji, 1 P, jayati, to defeat; surpass, excel]
[ma~ng, 1 U, ma~ngati/te, to go, move; appear beautiful]
[kam, 10 A, kAmayate, to love, be enamoured with; to wish for; kAntiH = beauty]
[bhUSh, 1 P, bhUShati, 10 U, bhUShayati/tE, to adorn, decorate]
[arth, 10 A, arthayate, to request, beg; to desire, strive for]
[Because prajA is strIli~Nga, prArthinI instead of prArthI]
[shR^ii, 9 P, shR^iNAti, to tear to pieces; hurt; to wither away, decay]
[pad, 4 A, padyatE, to go, approach; attain; observe]