This is proof that you've honed a certain Support Talent enough to be able to teach it to others at the inn. Those who can, do. Those who can even better, teach!
This is proof that you've become quite familiar with the Library. How to obtain this is kind of a secret, but if you take the time to do a bit of reading now and then, you should be pleasantly surprised.
This is proof that you've stayed at inns for a total of 10 nights. Resting at inns can give you extra skill effects in battle thanks to mysterious ingredients in the meals you're served. You can also engage in chitchat with your companions and restore your initial SC to 100. Such hospitality!
Either on (at least) your 2nd playthrough or in Hard (or greater) difficulty, conquer the fierce battle at Falkewin Hillside without using any items! It's a steep challenge, but you've got what it takes!
This is proof that you've acquired equipment with a doubled skill from an enemy drop. Very difficult unless you're playing in Hard difficulty or higher! There's a rumor that offering sanctified equipment to a Lord of the Land may increase the chances...
This is proof that you've equipped items that activate an Elemental Union bonus skill. Basic skills all correspond to one of five different elements. Equip skills of the same element that line up directly adjacent to each other, and you'll form an Elemental Union based on how many skills are in the line. Check it out on the skill sheet!
This is proof that you've equipped items that activate a Stack bonus skill. You can get Stack bonuses by equipping more than one copy of the same skill at once. The more copies of that skill you equip, the cooler your Stack bonus will be!