General Courage:
* Bold
* Courageous
* Daring
* Fearless
* Gallant
* Intrepid
* Valiant
* Heroic
Facing Danger:
* Audacious
* Dauntless
* Stouthearted
* Unflinching
* Undaunted
Facing Difficulty:
* Resolute
* Tenacious
* Determined
* Strong-willed
Facing Criticism:
* Assertive
* Confident
* Self-assured
Other:
* Noble
* Strong
* Powerful
* Mighty
The best synonym to use will depend on the specific context.