Here is the full list of all 9 Broforce trophies - there are 5 bronze, 2 silver and 2 gold.
Finish the Ironbro campaign
Finish the campaign on hard
Finish the campaign
Kill a terrorist with a returned grenade
Kill a terrorist with a deflected bullet
Kill a terrorist with a martini
Kill 10 terrorists with a single turkey bomb
Literally punch Satan so hard that he explodes
Throw Satan off a cliff as Brommando