User blog comment:Eemam/Burst Frog/@comment-24277289-20150210161747

There are a bunch of ways to get burst frogs. You can save your Honor Points and summon them from the Super Honor Summon if it is going on, you can get them from the Daily Gifts, you can get them from special giveaway offers, you can get them as rewards from Frontier Hunter or the Daily Quests, some Bonus Quests give them away, and some other rare dungeons give them out as rewards.

Your best bet would be Daily Gifts since all these other things are rare events.