Thalia actually is first introduced in the series by her FY! moment, i.e. her stand on Half-Blood Hill that allowed Grover, Annabeth and Luke to make it safely to camp though it cost her her life. Zeus was moved by her sacrifice and heroism and transformed her into a massive pine tree which served as a guardian for the Camp even after she was freed from it.
Being a Half-Blood and a daughter of Zeus, Thalia of course has many more FY! moments than this!
My favorites are when she is tempted by ultimate power and the prophecy. The temptation is almost too much for her but what does she do? Joins the Hunter's of Artemis to become immortally 15. Way to dodge being a tool of prophecy!
I also loved her return in The Last Olympian. Though her bad ass-ness wasn't really shown it was awesome to see her again.