Jet on Sky Missions
First you must complete the Free Mission at Shinjuku, after you comple Chapter Thirteen. Once the Free Mission is completed, a Jet will be unlocked that can be used during Sky Missions.

When you want to select the jet scroll all the way down on the Dragon Select menu (past the Chaos Dragon) and you'll find a "???" option. Select it, and in the mission you'll be flying the Jet
Attack through walls
During any ground mission if you see enemies on your radar on the other side of the wall, you can begin your run attack until you see the flash that you are going full speed. Then press the attack button to send your attack through the wall, killing the enemies on the other side

Easy Weapon Leveling
To level up weak weapons quickly, go to story mode, chapter 1, verse 2 (to the castle) on easy mode. Equip Spiked Wisdom, Butcher's Joy, or another weapon that's magic creates an aura around you that can quickly kill enemies. Charge up the magic meter, cast the spell, then quickly press/hold R2, switch weapons to the one you want to level up, and then run around at enemies. The aura will kill enemies for as long as it lasts while the kills go toward the currently equipped weapon. Once the aura runs out, just switch back and repeat