Matsuri: you have two end-of-stage bonuses (based on time and max chain hits), what I did was to chain a lot, which tends to happen around the final stages, because the enemies usually survive longer and keep sending fiery enemies (even more during Fevers), which help you maintain your chain through the waves of stage enemies. A chain is started as soon as you destroy one enemy with shot (it's okay to weaken some of them with shot first), however, unlike PoFV, the hit chain isn't reset if you destroy another stage enemy with shot during your chain (most of the times it means not "perfecting" some enemy waves, depending on the situation, but it's very rewarding if there's fiery enemies being destroyed near the top center of the screen, and as they stop coming, your chaining would end if you didn't destroy another incoming stage enemy, which in turn keeps your chain going for a little longer)
There are some benefits for "perfecting" enemies, which I don't remember very well (filling your gauge faster may be one), but I think that it helps your survival more than your score.. (I think that if you manage to perfect consistently, the stage enemies on the opponent side become faster)
Also, there's the boss summon trick, which helps your survival: 3 (or more) flashing fiery enemies that are destroyed through chaining (this means, not directly) make you summon a boss, or counter a summoned one. Each time a boss is summoned, it becomes more difficult, so look for these 3 flashing enemies, even if you already have summoned a boss (because if there's already a boss on the opponent's side, the summon results in a lvl 3 attack instead), and, of course, try to avoid sending them to your enemy
