Daily Battle Incubators are incubators rewarded for defeating individual creatures in PVP, even if you lose the battle!
To find the Daily Battle Incubator, tap on the "Battle" menu and tap on the "Defeat 10 creatures" button on the upper right. To make progress, participate in PvP battles and gain Victory Points, which are given out for every opponent creature you defeat (up to a maximum of three per battle).
After collecting your Daily Battle Incubator, a 24 hour cooldown timer will show how long before accumulated Victory Points will start being credited again towards unlocking the next one.
You can only save up to two Daily Battle Incubators without opening them. If you have two saved up from not collecting them in previous days, additional Victory Points will not be credited towards a new Daily Battle Incubator.
As part of their perks, VIP subscribers will also receive higher quality rewards from Daily Battle Incubators as opposed to non-VIP players.