This page of our guide to Judgment you will show you how to earn a large amount of experience and quickly develop the character. Takayuki Yagami's development is crucial - you will do better in combat and be more efficient during investigations.
There are several ways to get quite a lot of experience. Story missions give you the most SP - you get more of them as you progress. Subsequent story chapters give you more SP from story missions.
Another way to gain experience is to perform tasks found in the KamuroGo app. There, you will find many challenges that reward you with SP. For example, eating meals in a restaurant, getting high scores in mini-games or getting friends rewards you with a certain number of SP. Keep that in mind when you decide to develop Yagami.
Take your time with the development of the hero - there aren't many options to get some of the skills prematurely. You need to systematically complete the basic mission - KamuroGo challenges can be done in-between them. Thanks to this, you will get enough SP to develop your hero.