Time Shards
The player is rewarded for time traveling by being given a number of Time Shards.
The amount of shards awarded depends on how far the player progressed in that run before time traveling. Every Godzilla defeated, every kaiju beat and every monster wave obliterated adds to a hidden point tally that factors into that reward. These are all weighted differently, with Godzillas giving a lot more points than defeating a regular kaiju while monster waves contribute little to the total. That point total is then multiplied to give the player a number of shards, with that multiplier going up the further they progress into the run.
Putting this into practice, when time travel is first unlocked, defeating Godzilla might move your Time Shard total from 19 to 21 around stage 121 while defeating a kaiju will move this total by 1 shard and monster waves less than 1. However, by stage 1523-1525, defeating a Godzilla will move this total by 30 shards, defeating a kaiju by 18 shards and then a monster wave by 3 shards.
The Time Shards to be awarded are recalculated every time an adversary is beaten. As a result, it doesn't matter what order the player progresses in the game. A kaiju beaten on an early level of Tokyo is worth the same amount of points as a kaiju on the Moon. What does matter are the final tallies, meaning the total number of opponents defeated of the various types possible (Godzilla, kaiju or monster waves).
Below is an example, showing the immense progression possibly the further the player gets into a run.

Note that on this screen, which is shown just before time traveling, the data is a mixture of totals and stats related to the current run. The defeat data for number of Godzillas and kaiju are totals, across all runs you have ever done. The stage number listed, though, is for the current run only. For Version 2.3.3 onward this was changed so that the number of Godzilla and Kaiju defeated are also just for that current run.
Before time traveling, an opportunity, for a cost of 300 X-nium, is offered to double the amount of Time Shards awarded in a run. |