We will honor the task given us and give it our all.
Tips
usage
Formal praise for someone completing a significant assignment — usually diplomatic, military, or organizational missions. Not for everyday tasks. Often follows 顺利完成 or appears in reports.
grammar
Literal: 不 (not) + 辱 (disgrace) + 使命 (mission). 辱 here is a verb — 'to bring disgrace upon.' The structure says: 'did not bring disgrace upon the mission.'