[Baertram]

You need to find out which scene is used as the achievements are shown.
Use a tool like merTorchbug or zgoo and inspect SCENE_MANAGER -> currentScene as you are at the achievements.
Find out how to call that scene to show the attached fragemnts and controls.
e.g. this shows the set collections:

 MAIN_MENU_KEYBOARD:ToggleSceneGroup("collectionsSceneGroup", "itemSetsBook")

Maybe there is something simialr for the achievements.
I think it is defined as "achievements" here:
https://github.com/esoui/esoui/blob/...ments.lua#L972
Could work to show it via SCENE_MANAGER:Show("achievements")

Edit:
Here you see what I mind with the game menu:
https://github.com/esoui/esoui/blob/...ents.lua#L1345
This should be your code that you want to use. Checks if the achievement scene is not shown and then queues and shows it.

And for the searchbox you need to find the control for it via moving the mouse above it and use /tbugm or /zgoo mouse.
You can then searhc it within the achievmetns code.

But I think this already looks promising:
https://github.com/esoui/esoui/blob/...ments.lua#L984

Within the init of the Achievements there is ACHIEVEMENTS_MANAGER:SetSearchString(self.contentSearchEditBox:GetText())
selfshluld be ACHIEVEMENTS so ACHIEVEMENTS .contentSearchEditBox shuld be the search edit box where you need to set the text vis :SetText()
And this would then call the attached "changed" handler function, or you manually need to call ACHIEVEMENTS_MANAGER:SetSearchString(self.contentSearchEditBox:GetText()) as well.