"Life ambition" refers to a person's biggest goal or aspiration in life. It is the one thing they strive to achieve or accomplish throughout their lifetime. Full definition
We can not expect them to abandon their quality of life ambitions. (worldcoal.org)
To oversee the work they tapped Jackson, chief calligrapher for the queen of England, whose life ambition was to produce a handwritten Bible. (religion-online.org)