常に means “always”. You can also say いつも instead but 常に sounds a bit more formal. In many cases, 常に and いつも are interchangeable, but there are times when you can only use いつも. It is when talking about a habit that takes place on a regular basis in a certain condition.
胸を張って means “proudly” or “confidently”. 胸を張る is a verb literally meaning “to push your chest out” which makes you look confident and this te-form of the verb means “in a certain state”.
生きろ is the imperative form of 生きる meaning “to live”. This form is used to give an order or command to people in a lower status or equal in male speech.