Here is the full list of all 13 Rain City achievements.
Talk to the apartment owner more than 10 times
More than 90 points on the drum game
More than 100 points on the drum game
Succeeded with the crane on the first try
Succeeded with the crane within five tries
Scared the rabbit 10 times
Cleared the maze on the first try
Tried the maze more than 10 times
Unlocked the locker chain on the first try
Tried to unlock the locker chain more than 10 times
Avoided two trucks in the mine
Cleared the boss battle on the first try
Died in the boss battle 10 times