Introverted Intuition (Ni): Early on in the series it becomes clear that Annabeth is a planner. She is constantly stratagizing and thinking ahead in order to gain advantages in whatever she does. While Percy leaps before he looks, Annabeth looks before she leaps. Annabeth has many ambitions and holds onto them over time until they are realized. She dreams of being an architect, and eventually she achieves her dream. When there is some obscure fact that might come in handy, chances are Annabeth knows it. She collects information not just because she finds it interesting, but also because it could be useful. Annabeth has a tendency to figure out secrets based on very little information, such as the time when she figures out who really orchestrated the lightning bolt heist based on only a few scattered facts. Annabeth sees the shades of subtlety that Percy misses. While Percy is extremely aware of his environment, Annabeth is able to read between the lines and fill in the gaps that her observations leave.
Extroverted Thinking (Te): While she has unrealistic ambitions such as getting her parents back together and saving Luke, Annabeth is strictly practical in her actions. She approaches problems pragmatically, finding practical solutions that will get her the results she wants and abandoning things that she can't change. While Annabeth is clearly charismatic and takes command easily , she is clearly not an ENTJ. She is usually content to advise and work behind the scenes, passing off command to Percy when she thinks that he knows what he's doing. Annabeth is extremely capable, running away from home at the age of seven. She is realistic in her assessment of herself, but doesn't hesitate to do what needs to be done. She takes action decisively when need be, after establishing her objective.
Introverted Feeling (Fi): Underneath a calm and calculating exterior, Annabeth is passionate about many things. She makes her standpoint clear in most situations, getting almost as upset about injustices as her xxFP friends. Before she smooths things out, her relationship with her father leaves her angry and bitter She tends to keep to herself, not because nobody likes her, but because she reserves her attention for a few select people. She is quietly but passionately loyal to the few people who she devotes time and energy to.
Extroverted Sensing (Se): While Annabeth looks before she leaps, she typically only looks once before taking decisive action. She is completely comfortable in situations that require physical exertion such as combat and has trained herself into an extremely dangerous warrior. She enjoys activities like capture the flag and chariot racing, combining her strategic approach with her athleticism.
Can we just take a moment to appreciate that spellcheck wants to change "Annabeth" to "Annabel." Just thought I'd mention that.