What is the highest achievable score in Catan
The game ends when you reach 10 points on your turn, so if you are playing with 5 or 6 players you could easily get high then 10 on the special build phases so it would be closer to the maximum number of points possible with the amount of building you have. 

5 point for settlements 

8 points for cities

4 for longest road and largest army 

5 in hidden victory points
So in theory you could get to 22 points if you are extremely lucky.   

taken from the rule book on ending the game:
"If you have—or reach—10 victory points on your turn, the game ends immediately and you win! You can only win during your turn. If somehow you find you have 10 victory points during another player’s turn, you must wait until your next turn to claim victory"