Learn your instrument(s). Playing advanced mariachi songs requires that you have a close personal relationship with whatever instrument you plan to use most often. If you plan to play more than one instrument (for a studio recording, for example), you should have an in-depth knowledge of how each of them work and sound.
Start with the basics. If you don't already have a basic knowledge of the mariachi style, learn about it. In addition to learning about the structure of beginner mariachi songs, acquaint yourself with the culture that the mariachi tradition was born from. This will make you a respectful and well-rounded mariachi enthusiast.
Practice as often as possible. Make it a habit to play your instrument of choice several times a week, or whenever you have a slot of free time. If you play more than one instrument, switch occasionally to keep your practice sessions varied and interesting. This will also improve your overall skill as a musician.
Track your progression. As you practice, you will find the basics becoming easy for you. As this happens, move on to more complex and challenging songs. Listen to the best mariachi recordings you can find to inspire you.
Seek out fellow mariachi enthusiasts to practice with. If you surround yourself with other talented musicians, their skill and style will be a great influence. It may also provide you with opportunities to perform live.
Begin practicing advanced mariachi songs when you feel that you're ready. Once you have mastered your instrument(s), the basics, and the more intermediate songs, you should feel comfortable enough to approach an advanced mariachi tune. Playing it with a group will encourage and reinforce your efforts.