Well folks here be the last LoZ respect thread I do for a character, that many probably think is just like Peach....but she really, really isn't, not even close. So folks, let us get into it shall we?!
The Princess succeeded in breaking the barrier around Ganon's tower using the power of the Sages- Taken from Hyrule Historia
Can break magical barriers.
Midna began collecting the Fused Shadows, however she was attacked by Zant, who stole the shadows and left her on the brink of death. The Hero met with Princess Zelda and she poured all her power into Midna, saving her life- Taken from Hyrule Historia
She saves Midna's life who was near death after being attacked by Zant, who was pretty powerful himself.
Once Princess Zelda's spirit, which remained in Midna, returned to her body, she defended Link using Light Arrows- Taken from Hyrule Historia
After going back to her body, Zelda gained Light Arrows and helped Link with defeating Ganondorf.
Link and the princess, to whom the future had been entrusted, launched a final attack on Ganondorf. Ganondorf fell to the power of Zelda's Light Arrows and the ability of Link's blade to repel evil, and turned to stone- Taken from Hyrule Historia
Straightforward really, like above Zelda shows to be a capable archer and helps Link to defeat Ganondorf.
Zelda is able to contact Link via telepathy
Here she is able to break free from a crystal that Agahnim trapped her in.
Here along with the other 6 Sages, combines her power with the other to seal away Ganondorf. She is the 7th Sage, leader of them all.
Zelda combing her power with the 4 sword Links, to seal Ganon away within the sword.
Here she is able to defend herself from previously sealed monsters, even Vaati acknowledged her as a threat to him.
The Princess of Hyrule, said to have mysterious powers. Afraid Princess Zelda would get in his way, Vaati turned her to stone- Taken from Hyrule Historia.
Just really re-iterating what the scans show up top.
With the Sages power she is able to look into the past.
She is able to recall events from the past(over 100 years ago) thanks to the Triforce of Wisdom, she also states that she'll pick up a sword to fighting Ganondorf if need be(though we don't have a full knowledge of what her capabilities are with one.)
She is able to resist Ganondorf's body possession of her from killing Link(who wasn't about to hurt her)
Noted by Ganondorf to be quite the archer and that she shouldn't be taken lightly, eventually landing an arrow shot on him.
She is able to teleport from Ganon to Lon, Lon Ranch.
She rescued Princess Ruto from underneath ice, when Zora's domain was completely frozen.
Treated Link's wounds after a short battle with Volvagia and falling off a ledge.
Here she moves fast in a blur to cut one of the Twinrova sisters before they are even visible.
Here she is turned into Sheik by Impa and also more than likely trained by her aswell for 7 years, Impa herself being a Sheikah whom are a clan of ancient ninja warriors sworn to protect the Royal Hyrule Family.
Just to give an understanding who trained Zelda. Impa was able to avoid a punch by Ganondorf, carrying Zelda with her and while she kept Zelda close with one arm, she was also able to fight off Stalfos who had been slaughtering Hyrule guards. She then 7 years later, was able to take Link by surprise and knock him down. Impa was also chosen by the goddess Hylia to watch over the seal of the Demon King and was able to seal Bongo Bongo for a time, Impa is also the Shadow Sage.
Able to form fire barriers.
Using a deku nut as a flashbang.
Well there you have it folks! Princess Zelda/Sheik! Enjoy!