To unlock the Climbing the Ladder trophy in FIFA 19, you will need to reach division 4 in Ultimate Team Rivals.
Rivals is the main versus game mode in Ultimate Team. After each match, you will earn skill points based on your performance. A win will generally reward you with +30 skill points, a draw will be a small + or - of anything from 2-8 points, and a loss will result in around -30 skill points.
To reach division 4, you will need to earn a total of 1,250 skill points (recently reduced from 1,600).