Usage patterns
〈人〉が意気込みを見せるfor someone to show enthusiasm/determination
The new player showed his enthusiasm in his first game.
意気込みを語るto speak about one's enthusiasm/ambitions
The coach spoke about his ambitions for next season.
〜という意気込みでwith the resolve/attitude that...
He trained with the resolve that he would absolutely win.
意気込みが伝わるfor one's enthusiasm to come across/be felt
His speech conveyed a strong sense of determination.