What are some hard challenges Katniss and the others fear?

Katniss and Peeta fear that people will come to understand their relationship (love) is a sham.

Katniss must convince the people in the districts she tried to take her own life because she was temporarily love-sick.

The group has to fight against President Snow, who wants them dead. Everything is set up so that Katniss will die (by Snow).

Katniss is challenged with the job of teaching the women in her district to hunt so they can survive.