the best way to do this was to become a flight attendant.

第一个不定式,只是做定语的,修饰way,也就是说,去掉都行
第二个不定式,是做表语的,谓语动词是was,be to do 的句式是将会
to become 不能改成becoming,因为不定式表将来,说明他没还有成为空姐,动名词的意思是他已经当了空姐,空少了