1) Determinedly 2) With ambition 
• (adv.) In an ambitious manner.
Am·bi'tious·ly adverb In an ambitious manner. 
[adv] - in an ambitious and energetic manner
ambitiously 1. A description of someone who has an earnest desire for some type of achievement or distinction; such as, power, honor, fame, or wealth, and the willingness to strive for its attainment. 2. In a manner showing the desire for personal advancement and may suggest equally a praiseworthy desire.
determinedly 1 with ambition adverb in an ambitious and energetic manner; `she pursued her goals ambitiously`