How to fix precession in pedal axle?
You have a loose bottom bracket. It needs to be replaced.

You need to buy a new bottom bracket, along with two special tools: A crank puller and a bottom-bracket tool.

If your current bottom-bracket is cup-and-cone style (I'm betting it is), it can be removed with basic tools and elbow grease. If it's cartridge style, it can be removed with the BB tool.

Here are links to all three at Amazon:

BB

BB tool

crank puller

Or, you could take the bike to your LBS and have them handle it. This is a common operation and probably wouldn't cost much.