首先,那个himself应该是herself
句意为：已经下定决心要成名的女孩没有接受来自她父母的任何帮助.
至于用determined的原因是因为事态是过去时
原句可以=The girl determined to make a name of herself and didn't accept any help from her parents.
附：make a name 成名; 出名
例句：
I will make you a great nation,and make your name great,and you shall be a blessing
我必叫你成为大国,使你成名,你将成为有福之人.