【Invincible】 , 【unconquerable】 ,  【indomitable】 ,  【impregnable】 ,  【inexpugnable】 ,  【unassailable】 ,  【invulnerable】  mean proof against attack or defeat.

A person or thing is  【invincible】  or  【unconquerable】  that presents insuperable difficulties to his or its being overcome or displaced;  【invincible】 , however, usually implies a quality or character in the person or thing which makes him or it actually or seemingly incapable of being vanquished;  【unconquerable】 implies rather the fact of having successfully resisted all attempts at subdual or mastery.

A person or a human quality (as mind, will, or energy) is  【indomitable】 that stubbornly and determinedly resists all attempts to gain mastery over or discourage him or it or endures seemingly insuperable difficulties with fortitude until they are overcome.

Something material (as a fortress) or intangible (as virtue) is 【impregnable】 when it is strong enough or sufficiently guarded to repel all attacks or assaults.

A thing is  【inexpugnable】  or  【unassailable】 either because it is 【impregnable】 or because it offers no point at which it can be attacked or no occasion or reason (as a weakness or a defect) for attacking or impugning.

A person or thing is  【invulnerable】 that cannot be wounded or penetrated by a destructive weapon or piercing instrument.