Srimad BhagavadGita

In the previous śloka, Kṛṣṇa explained to Arjuna that if he did not perform his duty of fighting the war, he would not only lose the benefits that the war would bring in this lifetime and the following lifetimes but also incur great sin whose result will have to be experienced in the next lifetime. In this śloka, Kṛṣṇa tells Arjuna that in this lifetime too he will have to face infamy. Kṛṣṇa says, "Everybody at all places and at all times will speak of your infamy. For someone like you who is greatly honoured for your qualities like courage, valour etc, dishonour is worse than death." 

akīrtiṃ ca The term akīrtiṃ does not just refer to 'being deprived of fame' but to its opposite which is infamy. The 'ca' here conveys the meaning that, 'O Arjuna, in addition to losing out on the benefits in this lifetime and the next and incurring great sin to be borne in the next lifetime, you will be defamed in this very lifetime. You will have to hear things about yourself like, 'Soon after the war started, incapable of action, Arjuna turned his back and ran away'  

avyayām (This Infamy will remain forever without getting destroyed) Since Arjuna's fame is spread across all the places, his infamy will spread alike and will be un-erasable. 

bhūtāni api kathayiṣyanti (Criticism will come from all the people irrespective of their capabilities) Criticism coming from the strong and valorous can still be tolerated but here criticism coming from all kinds of people will have to be tolerated. Incase Arjuna would respond by saying, 'Let people speak as they like, I don't care', the second half of the śloka serves the purpose of addressing this response.

ca The 'ca' in the second half of the śloka serves as a convincing answer to this.

saṃbhāvitasya For someone like you who is glorified by the strong and the ordinary alike for your valour, strength and for being the greatest archer of all times.

akīrtiḥ maraṇāt atiricyate (Dishonour is worse than death)

Q: When statements from the Mahābhārata like jīvan bhadrāni paśyati Mahābhārata Virāta Parva 38.44 (Staying alive will bring auspiciousness) and ātmārthe pṛthvīṃ tyajēt Mahābhārata Udyōga Parva 127.49 (One can even abandon his own motherland that protected him) say that for saving one's own life anything can be given up, then why is it said here that one must give up his own life to safeguard his honour?

A: These instructions are applicable to ordinary people, and not to kṣatriyas who regard their honour to be more precious than their lives. Moreover this is going to be no ordinary accusation. Per Lord Rāmā's statement akīrtirasya gēyet loke bhūtasya kaśyacit | patatyevādhamān lōkān yāvacchabdass gīyate Rāmāyana U 45.11 (A person who is defamed in this world surely goes to hell. Until the word remains he will be at loss), For a kṣatriya, while dishonour leads to hell, death on the battlefield leads to the honour of heaven.

Hence, for a kṣatriya like Arjuna it is undoubtedly better to give up his life in the battle rather than be defamed.