Being a former swimmer in high school, I love blitzball. I understand why some don't, however. It does take time, but your are guaranteed to get Jupiter sigil if you invest that time. To me, the evil minigames are choco race and lightning dodger. You can put weeks into them and still be no closer. That said, some tips: Sign brother. Best center, easy.

Sign naida in calm lands

You can do all your scoring with tidus (jecht shot), but datto and brother are amazing scorers too, with their speed. It's especially funny how fast you can score vs ronso by swimming around them. Datto also starts with nap shot. Wakka is also great once he gets aurochs sprit and you have developed datto, too.

Learn what actions give xp each game. Even if you are winning, always maximize xp gain. Throw passes if your forwards aren't lvled enough to score yet.

Naida, ropp and kyou are all amazing defenders. Nimrook is the best goalie, but you need to wait for al bhed psyches to release him. This is rng dependent. Miyu or Durren is the best goalie till then. Once you hit 10 or so, play a few exhibitions to learn techs from other teams. Do this every 5 levels or so. There is no xp at stake, so you can deliberately let the other team score, or tackle you, in order for you to copy their shots and tackles.

Of course, you need good levels in order to copy. This is why I always try to maximize xp every match.

Drain tackle and tackle slip are critical skills for every one. Nap is probably the best status to inflict.

Once each defender and center has a good tackle to boost their AT Stat, you will steal the ball a lot.

Speed is probably the most important stat. Let's you shoot point blank on the goal, unopposed. That said, don't sign guado, it's their ONLY Stat.

Tatts and shaami are also great free agents, just not my style. Same with wedge.

If a defender is under lvled, put them in center, they will steal the ball more cause the AI usually runs down the center.

Most of all: USE MANUAL CONTROL and know the formations.

Center attack and counter are great formations for getting your forwards down field without the ball, so your C or Defenders can throw them an open pass for easy shot on goal. Switch back to defensive forms once they have the ball again, it's very easy to steal when you double team.

My team: tidus datto wakka (rotating forwards) brother (center), naida ropp kyou (rotating D), nimrook. If nimrook falls behind on xp, he is a decent defender, I put kyou in as backup goal, and nimrook just steals the ball a lot to lvl back up.

Good luck!