See my Tauriel essay for scene details. For clarification on how the eight functions work, see here.
Dominant Te: Tauriel hates inefficiency. She constantly wants to act – whether it's attacking Dol Guldur or entering Gundabad. Her decisions are based on logic, not emotions (her speech to Legolas has very little emotion based statements). Tauriel is both direct and blunt. She is in a constant power struggle with Thranduil, who is also an ENTJ.
Auxiliary Ni: Tauriel relies heavily on her instincts. She intuitively knows that more spiders will come, because of the behavior of the present spiders. She is always looking towards the future and wants to redesign their system of fighting the enemy. She is abstract (view of stars, conversations with Kili).
Tertiary Se: Tauriel is able to adapt quickly in physical situations.
Inferior Fi: Tauriel has very strong internally based morals. However, she is not great with actual emotions. She is confrontative and doesn't hesitate to lash out and do verbal battle (against Thranduil twice (and one nonverbal, during the orc interrogation), Legolas once, and the orc once). She doesn't mince words with Bain. She believes she is right, and doesn't take the time to try and understand other people's viewpoints. She is scared of her love for Kili. All of this is her Fi coming out through her Te.