The following comes courtesy of Brazilian site Judao.com via Trek Movie. There are detailed highlights of 38 minutes of the movie - mostly from the beginning but some stuff later on also - including set pieces and some character stuff too. No deaths are given away or anything, but if you don't want to know anything about the film before seeing it I wouldn't read any further.
Nibiru mission ends with Kirk rescuing Spock by violating the prime directive by revealing the Enterprise to Nibiru natives so he can beam Spock out of the Volcano
Kirk has a scene in bed (back in San Francisco) in bed with two "cat women"
Kirk makes mention of hoping to get assigned to a "five year mission" (implying that the famed five year mission hasn’t started yet for the time he has been captain)
Kirk is demoted for violating prime directive on Nibiru, loses command of Enterprise with Pike to take over command Kirk as first officer
Pike wanted to send Kirk back to Academy but was convinced (possibly ordered?) to make Kirk first officer of Enterprise by Admiral Marcus (played by Peter Weller)
Spock assigned to another ship
The "father" character uses his Starfleet ring as a bomb (dropping it into water for a reaction) and destroys a facility (in London)
London attack leads to big meeting of Starfleet captains which itself is attacked by John Harrison, resulting in Pike being injured…Harrison transports away
Later scenes in the film….
Enterprise severely damaged falling to Earth with Spock in command ordering evacuation
Kirk and Scott seen in Engineering trying to stabilize ship
Later Spock scene beaming down to San Francisco and starting long chase with Harrison
Eventually Spock meets up with Harrison and engages in a fight
Source