And so he died.

Bridge - There are many meanings that you could give to this symbol. The details in the dream are just as important as the bridge itself. The first consideration should be given to how much he travels. The bridge can be interpreted literally if it is a part of his daily commute.
On a more psychological level, bridges can symbolize transitions (e.g. transition from one stage to another, from one level of consciousness to another). Since most bridges are over water (i.e. emotions, unconscious), this dream could also be symbolic of him rising above his emotional difficulties or subconscious drives.

Unknown woman - an unknown, or unacknowledged, feminine side of 'the self'. We all have a masculine and a feminine side. The masculine side would be the part of ourselves that we view as brave, strong, stubborness, logical...etc. The feminine side would be the part of ourselves that we view as emotional, nurturing, tender, sensitive etc.

Hair is highly valued by most cultures. It is symbol of vanity, security, sensuality, sexual appeal, and of youth. In some cultures women are not allowed to show their hair outside their homes. Wealthy men go through painful surgery and spend thousands of dollars to replace lost hair follicles. Needless to say, hair is a valuable dream symbol. It represents physical and spiritual strength. Samson's hair was the source of his strength and virility. In our dreams hair can represent our thoughts, knowledge, and reasoning. White or gray hair represents age and wisdom while body hair may symbolize protection and warmth.

Long hair - symbolizes freedom, luxury. Also permissiveness.
Dark hair - represents the unconscious area of thoughts and attitudes. Also 'dark' thoughts or attitudes.

Running away from something - Something in the his life is difficult to face, and he would rather run away from it than face it.
Because it was 'the woman' (his feminine side) running away suggests the something was an emotional issue of sorts.

Being chased by something - When we have a dream that something is chasing us, it can mean that we feel a threat in our waking life. He needs to try to figure out what, or who, the thing chasing you reminds him of.

Runs with her(rescue) - This symbolizes his leadership qualities. That he sees himself as a leader rather than a follower. Also represents the type of examples he sets for others to follow...or advice he gives.

Fights the creature - A fight may represent a conflict in a real-life domestic or work situation.

The conflict may be within him, between opposing forces in his psyche. An obvious candidate, is a clash between what he wants to do, and what he feels he ought to do. In this case, bear in mind that the conscience is usually socially constructed and consists of the prohibitions and ideals that were imprinted in his psyche during his early years.

If the conflict is between his conscious ego and his subconscious, the aggressor in the dream fight will probably represent the part of him that is demanding release from the dungeons of his subconscious. 'It' will not hurt him unless he denies 'it' freedom of expression. He should try to identify it, and then welcome it as a talent or energy that can contribute constuctively to his well being. Change the conflict into a dialogue, a respectful exchange between his conscious and subconscious.

Where there is unresolved inner conflict, there is a tendency to project the subconscious protagonist to other people, or creatures, often with dire consequences in personal relationships.
More specific inner conflicts are those between opposite psychic qualities or forces, such as masculinity and femininity, thinking and feeling.

He is defeated - suggests he feels powerless over this emotion....or whatever the 'creature' represents.

He dies - Dreaming about death is very common and it can be interpreted in many different ways. Death is usually a symbol of some type of closure or end. It implies an end to one thing and a beginning of another. Death dreams usually have positive symbolism. It could imply that he would like to leave all of his worries and struggles behind and begin anew.
Does he know how he died in the dream?( Bitten, choked...etc) This might point to what part of his life is bothering him.
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Did he make a decision long ago that he regrets, or that may have caused something bad to happen?
Did he give up something, or 'some part' of himself, and he's regretting it?
Has he denied himself something, or opportunity, and it's bothering him greatly?
Was he(or a loved one) emotionally injured long ago, and he's angry about it, or felt he should have done something about it...but instead buried it or tried to forget it?

I hope this gives him something to go on, or sets him on a happier path.
Hugs & Happiness,
J