The fastest way that I have found to level up is to complete the final boss repeatedly. The chapter completion bonus boost from level 1 to 6 in one run. Takes about 4-5 runs to max out a ranger from level 1.
This method requires two controllers, one as your main account and a second for the ranger you want to level up. You can also earn revives as your low-level ranger will fall during the fight to earn the 30 for Healer.
For the zord fight. First, let the monster defeat you in tank mode. This is much faster than trying to defeat it. For the battle mode, both controllers need to complete all the inputs for you to complete your attack. I personally can't complete the 5 button sequence on two controllers but regardless you should win the fight.
If you have more than 2 controllers and some friends over, you can power level more rangers.
To max out the abilities go to 6-2 and alpha 5 is right at the start of the level. You can simply upgrade and then quit out after saving your upgrades.
Rinse and repeat and it shouldn't take long to get all 6 rangers to the maximum level.
Thanks to MkMaster13: You can pause during the quick time event in the megazord battle. This will allow you to memorize the buttons before input.