You ask a "relative" question. As in...do you have a rich relative that you can ask to get it repaired for you?....
KIDDING! JUST KIDDING!
But, the answer to "how hard is it" IS relative. For some it will be EZ. You are dealing with about the SIMPLEST form of transmission there is. Just a drive gear at the end of the main shaft and a forward gear at the front of the prop shaft and reverse gear at the back of the prop shaft with a simple "dog" clutch between them. here's the picture.
http://www.boats.net/parts/search/Honda/Outboard Engine/2000/BF50AY LRA/PROPELLER/parts.html
Once you take the prop and thrust washer off, bend back the ears on the "claw washer" (#19) that are securing the gear case nut (#7) and use the special "spanner socket" to rotate the nut counter clockwise and unscrew it from the case...the transmission will come out all in one piece except for the spring (#6) holder (#4) ball (#29) and the pin (#5). Those parts will probably "boing" out in the case and need to be retrieved but, as long as you know they are there, they ain't goin' no place and you can get them and put them back. As a matter of fact, that MAY be where your problem is. I don't know. But, the pin and the ball and the holder all can wear down and cause too much clearance.
If you're going to do this yourself, you NEED THE MANUAL. The HELM INC manual. AND THAT MANUAL ONLY. If you look at the parts list, you will see some "selective" parts. Meaning? There are SHIMS (#20) and (#21) that you will need to measure for so that the transmission works correctly when you're finished.
The socket for the case nut is necessary for REASSEMBLY purposes. So that you can TORQUE the nut to specs and have the SEAL hold and not leak water into your gearcase. Most of those nuts are frozen in there anyway and usually need to be CAREFULLY cut out so you can disassemble without the socket. Sometimes a healthy dose of PB Blaster and a pin punch and hammer can work to turn the nut to get it off.
As you can readily see, the cost for this job is NOT in the parts, it is in the LABOR and KNOW HOW. The problem here is that you really don't KNOW what's wrong yet. It could (and probably is) be something simple.
If you compare the price of the Helm manual (around $120 or so) and the socket ($60??) Vacuum/pressure test tool ($80??) That's a LONG way from $1200. The parts you need will have to be determined after you get in and take a look.
BUT...YOU HAVE TO DO THIS RIGHT... the first time! OR, it turns into a bag of worms with a leaky gearcase and ruined lower end.
Below is the picture of the lower shift rod and the vertical shaft with the drive gear on the end. Mostly I added it for reference. BUT.... Note Item 16..the "pushrod" That little item is what pushes on the "pin" that is on the prop shaft to shift into reverse. It can get a "groove" worn into it and cause the problem you're having. It's either a LOT of wear on one or more parts or the lower shift rod is badly bent for some reason.
I suppose it could be that the shift rod seal holder assembly (#17) could have come loose or broken in some way and is allowing the lower rod to "flop" around or deflect enough so that it can't push the shift pin properly. Those are the things you need to be looking for when you "go in".
Good luck.
http://www.boats.net/parts/search/Honda/Outboard Engine/2000/BF50AY LRA/WATER PUMP/parts.html