How many people did Katniss kill during her time in the 74th HG?

She killed Glimmer, the tribute from District 1 when she dropped the Tracker Jacker nest on her after the Career Tributes, plus Peeta, her District partner trapped her in a tree.

Katniss dropped a Tracker Jacker nest on the Career Tributes below the tree they trapped her in after the District 11 female Rue pointed out the nest to Katniss. The result of that was both Glimmer from District 1 and the other Career Tribute girl from District 4, had succumbed to the stings the Tracker Jackers had stung them with. That was her first 2 kills.

After Katniss and Rue planned to blow up the Career's supplies of food, Katniss heard Rue scream her name and Katniss had just reached her ally when the District 1 male, Marvel, threw his spear just as Katniss shot an arrow at his neck, killing him. Marvel had successfully killed Rue during the encounter. That was her 3rd kill.

During the final 3, after Cato had Peeta in a chokehold at the edge of the Cornucopia roof, Peeta signaled with his finger an X right over Cato's hand, to indicate that Katniss shoot his hand. After that, Cato fell to the ground and was halfway eaten alive by the now revived tributes as mutts. Then Katniss shot an arrow into Cato's head, signaling that the last tribute was dead. That was her 4th and final kill.

Overall, she's killed 4 people.

1st kill - District 1 female

2nd kill - District 4 female

3rd kill - District 1 male

4th kill - District 2 male

She's killed Marvel from District 1 (an arrow to the neck in the book and an arrow to the chest in the movie) and Glimmer from District 1 (tracker jacker stings in both book and movie).

She's killed Cato from District 2 during the final three by shooting an arrow to his head after he fell off the Cornucopia roof down to the ground below where the now reincarnated 22 tributes were as huge dog mutts, where they began to eat him alive before Katniss finished him off with an arrow to his head.

I don't think the death of the District 4 female was counted as a kill.

But Cerys, when Katniss dropped the tracker jacker nest on them, Collins specifically states that both Glimmer from District One and the District Four female were both killed.