Too young... sorry.
I also had one that woke at least every hour, sometimes every twenty minutes. And he did it for 18 months. It was really no fun at all.
What did I learn during this 18m hell? Well I learned that there actually isn't that much you can do past a point. You can look at awake times, have a good routine, dark nights, light days, blah blah and that certainly helps. But only to a point.
Nothing kept my son asleep. Nothing. We tried sleep consultants, even ended up at the hospital in despair. There was nothing wrong with him, he just didn't bloody sleep. They offered to drug him. We refused that (then regretted it...)
Now yes, you can probably train anything to do anything. The problem is what you have to do to achieve the result and whether that's something you can tolerate. I did all the things I could tolerate. Routines, all the advice, even controlled crying (that made it a million times worse by the way.) I couldn't tolerate shutting the door and leaving him till morning so we didn't do that.
How did we cope? Well we gave up. We gave up trying to make him sleep because we had zero control over it. Instead we changed what we could about our lives. We slept in shifts. We made sure each of us had a few hours a day to sleep. And that actually helped a lot.
He hated the cot so we co slept. That helped. Then we put him in a toddler bed in a baby proofed room and that helped Too. At 18m it was like a switch. Bang - from every fucking hour to through the night. Incredible- and absolutely nothing we did.
4 months is regression time and unfortunately you just need to hang on and get through it. It sucks massively (this was one of our every twenty minute times) but it will pass (honest.) make sure each of you does a shift every day to give the other one a break and make sure each of you does a long shift one day at the weekend.
They do, eventually, sleep. There just isn't much you can do about it for a while. My sympathies because I know how hard it is.