how can I update ipad air IOS 12.5 to the latest IOS

You can’t.

Your iPad Air 1 cannot upgrade/update beyond any version of iOS 12, currently at iOS 12.5.

The 2013 iPad Air 1, iPad Mini 2 and 2014 iPad Mini 3 have overall internal hardware that is too old, too underpowered and incapable of running all of the new, advanced and internal hardware resource intensive features of iPadOS.

Sorry.

If you need/want an iPad with an up to date iPadOS with access to current, updated apps, then you really need to seriously consider a new iPad model OR a much “newer” , used iPad model capable of running the latest iPadOS versions. There are plenty of newer, older iPad models that can run the latest, current versions of iPadOS.

Sorry & Best of Luck to You!

A first generation iPad Air can only be updated to iOS 12.5.

Apple ended major update support for iPad Air1 in September 2019. Whilst the iPad Air1 has since benefited from “point” security updates, it cannot be updated to iPadOS 13 (or any later major versions of iPadOS) as the internal hardware does not meet the minimum technical requirements (CPU and RAM) for newer versions of iOS/iPadOS.

Some App developers have dropped support for iOS versions preceding iOS 13.x for technical reasons (often because APIs or software libraries upon which they rely have been updated in the new version of iPadOS, making their App incompatible with earlier versions). 

Whilst many App titles remain compatible with your iPad Air1, if you want or need to access to Apps requiring the most recent versions of iOS, you’ll need to consider replacement of your iPad with a newer or current model that supports iPadOS14.

Sorry, I appreciate that this may not be what you were hoping to learn.

I hope this information provides helpful clarity as to your available options - and the limitations of your existing iPad Air.