Here is the full list of all 10 Sokoban Next trophies - there are 5 bronze, 4 silver and 1 gold.
Solved all puzzles
Obtained all stars
Perfectly solved all puzzles
Pushed 100 eggs in place
Pushed 500 eggs in place
Pushed an egg 1000 times
Pushed an egg 10.000 times
Walked 1000 squares
Walked 10.000 squares
Nearly fell off a ledge