Some details of the system aren't mentioned yet, so I'll go over them.
1) The bottom right gauge is filled by collecting colored crystals, and it acts as a fill multiplier (for the bottom left Border gauge) for the crystal of the other color. This basically encourages you to press C and swap characters when you're about to collect a large amount of crystals when the gauge is at high values, up to x3. This effect doesn't last very long at all, so you'll have to time it well.
2) Switching characters with the Reimu-Yukari combo (Border shottype) will cause Ran to stay for a while when switching from Yukari to Reimu. Switching characters with the Yukari-Reimu combo (Demon Sealing/Binding shottype) will make your shots more powerful for a short while, depending on how much the bottom right gauge multiplier is, up to a max of x2.5. This is kind of useful to quickly shoot down a problematic spell, for instance.
Your multiplier won't carry through stages, so try to make use of them during the boss fight.
Additionally, there's one more tip I can share: The Spell Card Bonus won't void if you Border Release before the spell display animation is done; in other words, you can still cap a spell if you Border Release before the SCB is displayed. This allows you to carry the Border Release effect into the first second or two of a spell, and then gives you a 25 second Border Sustain timer that won't count down. If you capture the spell, the 25s timer remaining will effectively refill all 3 levels of your Border gauge, making this trick highly abusable.
One last thing: graze doesn't increase PiV; instead, each graze gives 1000 points.