Been playing a few hours. I went down to the beach and grinded some on the monsters there, grabbed a bunch of Fish Fin, modded those to Water and junctioned that to STR. Most enemies were a joke after that. Then I got the Mid Magic refine ability and grinded a bit for Thunder, refined that into Thundara (and my Cure into Cura) and got even more powerful. I took down Ifrit pretty handily within 10 minutes and I was just about powerful enough to beat the mech boss but it revived before I got the final Thundara in. I shouldn't have Scanned that much to check on progress.
One important thing to note for beginners:
Everything is a resource in this game and everything can be modded into other things, so you can build your characters however you like.
Enemies can be turned into Cards. Cards can be turned into Items. Items can be turned into Magic. Magic junctions to improve any basic skill.
Enemies -> Cards -> Items -> Magic
So, you can improve your magic and thus your stats by:
fighting Enemies -> Cards -> Items -> Magic
or playing Triple Triad and winning Cards -> Items -> Magic
or even just ranking up your Seed Rank by doing exams, and getting tons of cash, and buying Items -> Magic
Then junction to STR if you just want to attack, or junction to MAG if you want to use magic. "But wait, I don't want to use magic, that will lower my stats!" you say. Well, when using these methods you will quickly gain a ton of different magic, more than you can junction at one time. Use the ones you haven't junctioned.
All of these options are viable, and you should only need to Draw a little bit in the beginning, when fighting bosses or just to grab some uncommon spells here and there. It really isn't a "Draw + Junction" system. It's a Junction system, and drawing is only your most basic way to feed into the Junction system.
