ProAntiTab does support 1.8.8 but requires Java 17 to do so.
You can achieve this by using PaperSpigot 1.8.8.
Just start your server with the following command line:
java -DPaper.IgnoreJavaVersion -jar paper-1.8.8-445.jar
Afterwards, go to your server.properties and set the option use-native-transport to false:
use-native-transport=false
Join my Discord if you require more specific help on how to do so:
https://discord.com/invite/fz88CKZXjg
Or feel free to ask in the discussions page/or send me a DM via SpigotMC. ^^
// Edit:
I've contacted the person via SpigotMC DM (private conversation) with an even more detailed description on how to run PaperSpigot 1.8.8 with Java 17 instead.
If anyone else requires help on how to run PaperSpigot 1.8.8 with Java 17, feel free to ask me. ^^