Can Alpha bosses be fought repeatedly?

Your first win over each Alpha costs no energy. Whether the repeat fights do is still open. That first defeat also hands you an Irisalis petal and a guaranteed set of evolution stones. There are 17 Alpha bosses, so the first clears are a one-time batch of rewards you collect by working through the roster.

After that, a fight is about drops. Alpha Aniimo drop the held items you need to finish a build, plus boss-specific materials for progression and evolution, evolution stones among them. Alpha challenge locations work as dedicated farming spots for these, and you can keep fighting Alphas for more Irisalis petals after the first one. Alpha Rookie challenges have no limit at all, so you can run those as often as you like.

Which Alpha bosses are worth farming

Some evolutions only happen after you defeat a specific Alpha variant of that species. For those, a repeatable Alpha is part of the evolution route and not just a source of loot.

The levels vary a lot. Alpha Stellarys is a level 18 Dark-type that appears on the map, in a field south of the Forest of Falling Stars. It drops Night Stones, and catching it is a way to get Stellarys early. Alpha Minespine is level 60 and sits in a hidden cave reached with Gravity Pull and explosive barrels. Some Alphas are large bosses meant for groups, so farming the tougher ones goes faster with other players.

Not settled: The game is inconsistent on the limit. Alpha boss challenges are described as repeatable without limit, but they are also tied to daily energy, and the first defeat is specifically the one that costs no energy. Expect repeat Alpha boss fights to draw on energy until this is settled. Alpha Rookie challenges are not affected.