Event Dungeons are limited time battles you can play. They are usually displayed before everything else.
There are currently four types of these events.
The harder and further down the story, the more base tickets you typically earn.
You can also boost the number of tickets by using specific Medaparts which gives your Medabot an additive boost to each stack you get from completing a mission. The amount of bonus you get is the highest point value Medapart on each Medabot plus Medafighter bonus (if any).
In point events, you typically grind a story battle over and over to earn points. Instead of a shop, your points are added to a cumulative total that rewards you with items at specific milestones. Typically, to earn the full Medabot set, all rubies and energy capsules, you need to accumulate 160,000 points.
The harder and further down the story, the more base points you typically earn, and a higher chance (but still very rare) to trigger a x2, x5, x10 or x20 multiplier.
You can also boost the number of points points by using specific Medaparts which gives your Medabot an additive boost to the base amount of points you earn. The amount of bonus you get is the sum of all eligible bonus-awarding parts or Medafighters.
Invasions are extremely difficult battles that do not reward you with anything (besides the ruby for a first clear).
These have been succeeded by EX Battles.
Advance Robattles is a multi-stage event consisting of multiple battles per stage. In each stage, you are not allowed to reuse Medaparts. This means if you use a Medapart in a battle, you cannot reuse it for a future battle within the same stage.
This resets once you clear a stage (complete all the battles in a stage).
EX Battles happen when none of the other four above events are happening.
Invasions are limited time glory fights that rewards nothing but first clear rubies and feature a set of novel bots for you to fight against.
Currently there are currently two recurring themes of events. Everything else is a one-time.
Super Battles are time-limited point grinding events featuring a series of character introduction cutscenes and battles that grant you event points.
Castle of Witches
Castle of Witches events are time-limited ticket grinding events featuring a side-story in Miruki's Witch Castle in the Medabot Theme Park on Medarot Island.