Overall hint: 
Nyy pebffjbeq nafjref ner qvssrerag jbeqf juvpu pna zrna “abguvat”.



All answers, in case you want one or more as a hint:

ACROSS

3. FDHNG
4. IBVQ
6. FPENGPU
7. ABHTUG
8. ONTRY
9. YBIR
12. MVC
13. QVPX

DOWN

1. WNPX
2. OBB
3. FUHGBHG
5. QHPX
7. AHYY
8. OYNAX
10. RZCGL
11. ANQN
12. MREB