You only need one, single berry (the only berry that is available) from this event. If you have more tickets after that, buy a feather (You'll need one of each color to make the base Indrik that you will later evolve into the Onyx Indrik). The other 3 Onyx berries will be made available at later events.

During each event when a new type of Onyx berry is available, buy the berry first, then a feather if you have more tickets. Always prioritize the berry, because they go away after that particular Indrik season/color, but you can buy more feathers during later events if you need them.

You do not have to make the Nascent Indrik before buying the berries. You can make the Nascent Indrik after you collect all 4 berries if you have to wait to get feathers. You will still be able to evolve the Nascent Indrik into an Onyx Indrik later as long as you have one of each Onyx berry.

To make the Nascent Indrik, you will need:
One of each color feather to make the base Nascent Indrik.

To make the Onyx Indrik, you will need:
One Nascent Indrik + 1 Onyx berry of budding + 1 Onyx berry of Bloom + 1 Onyx berry of Growth + 1 Onyx berry of Ripeness.

Once you have evolved your Nascent Indrik into a new color (in this case Onyx) the Nascent Indrik will disappear from your mount listing. If you want to make another color later (White will be available at the end of the year) you will need to repeat the process by making a new Nascent Indrik, then evolving it using that season's berries (for example, 4 white berries).

This link may help it all make sense:

https://en.m.uesp.net/wiki/Online:Nascent_Indrik