Palworld

This is for those who just want this to be out of the way fast.

Easy/Fast Way

Max out a Pal means to make it 4 star, the level or stats dont matter.
Easiest way to do the cheevo is to go to the start area and catch a lvl. 1 - 3 Pal 121 times from the same Species. (1 Star = 4 Pals, 2 Star = 16 Pals, 3 Star = 32 Pals, 4 Star = 64 Pals = 116 + 5 to max out)
Mix them all together in the Pal Essence Condenser to 1 Pal 4 Stars.
Once You have 1 Pal on 4 Star you can mix this Pal in another Pal to make it 4 Star instantly.
Repeat this with the 3 other Pals and you are done with the cheevo.

But remember you have to catch 1000 pals for another cheevo and for this cheevo you need to catch 585 pals anyway if you do it the Long/Normal way.

And also remember you can put stuff like Catch Rate and Spawn Rate up in your World Options to make this quicker.