The first thing we recommend you do is check your Internet connection and make sure it is stable, although in general the problem usually comes from the game servers, which may be offline, either due to maintenance, update or any other reason.
In this case, all you can do is have a little patience and wait until the developers take care of it and fix it.
That's all you need to know about how to fix error 429 in Apex Legends, so we hope the developers are already working on fixing this issue as soon as possible.