Relations (Apocalypse)
If a company likes aliens, they will hate you if you kill aliens.
Company A hates Company B AND Company B hates Xcom (Company A could be not-useful-to-Xcom)? Then Raid, Burn, Kill, Main Company A and Company B will like you. (This is a MAJOR hint if Transtellar hates Xcom)
Relations
yadda yadda...
Revenge
There are four major ways to exact revenge on a corporation if one feels that said corporation must be 'put in its place'.
General Raid
Quite easy to do, just assault the security forces with heavy firepower, killing all enemies.
Building Demolition
Use manual control of an air vehicle to destroy the city structure. (beam weapons are best)
Incendiaries
Burn! Use an Autocannon with incendiary rounds to reduce the tactical battlescape to ash. (real-time helps alot)
Controlled Demolition
High explosives Vs building foundations. (vortex mines are best)