what is the meaning of seeking the bubble reputation. even in the cannon's mouth.?(fighting relentlessly...)

 

'Bubble reputation' means reputation which is very momentary and bursts like a bubble.

“Seeking the bubble reputation. Even in the cannon's mouth.” 

These lines talk about that stage of the man when honour and pride hold importance for a man more than his own life. He cannot forsake and is very possessive about his reputation. He is jealous and strong enough to fight against anyone questioning his honour.