Possible Clues:

• What was shot? Golf course achievement accounting for handicap
• Double eagle giving handicap
• Actress Jessica sorts out Big Bird
• Largest-wingspan bird
• Southern hemisphere seabird
• Atlas bros alter the large bird with narrow wings
• A hole in one, perhaps, for mariner's dependant
• High-flier that's unusually below par
• Bird in brass -- a lot manufactured
• One was unlucky after shooting such a score, of course