Are all achievements needed for 100% run

The rules only say golden trophy needed

(If not is second adventure needed)

You don't need to do all the achievements to get the 100% of the Game, the 100% does only includes the completion of the Advventure Mode once, All Mini-Games, All Puzzles, All Survivals, like said in the rules.

There is, however, a category for all the Steam Achievements, which can be found here: https://www.speedrun.com/pvzce?h=All_Steam_Achievements