According to the Shulchan Aruch (please cite Saeef and Siman so I can read further):
What should one do when he's late to Shachrit? What should he skip and what must he say?
Shulchan Aruch OC 52 says to say Baruch she'amar, Ashrei, 2 of the הללו's, yishtabach and berchos kerias shema:
More Info: The goal is to say shemoneh esrei with the tzibbur. You need to say birchos kerias shema no matter what. Based on your time, you should try to say:
Also, you should say Berachos at the beginning, though if there isn't even time for that, you can just say birchos hatorah and e-lohai neshama before and the rest after.