300 trials might seem like a daunting task, but thanks to the large roster this game has...this ends up being a fairly simple task. For the fighting game novice I'd suggest simply going through the trials until you've done the Super Arts with each character. From here, test the waters and find out if you'd really like to keep going. Chances are even if you only go up to this point on every character you'll easily get the 300, though you might need to go a bit further for titles.
The links in these games are rather picky, it won't just be mashing things out like one might expect. This is the first thing you should keep in mind. They're all different, so try to keep yourself from growing frustrated if you can't do them right off the bat. There's a ton of trials available to you, chances are you'll end up doing more than you even need to for the titles achievement.