Props to Elem3ntal80 and TheBigBB for doing most of the legwork on this one, their combined solution of Rocky Ridge par 3 on amateur is the starting point for the solution I discovered (but did not see mentioned in the comments).
The stumbling block for this achievement is that you "can't use caddy skills or golfer abilities".
Problem is, this isn't strictly true. When I noticed that some putting challenges could be circumvented by chipping while on the green, I figured that the slightly wonky way the game keeps track of things could probably get you this achievement by assuming the rules can be bent somewhat. Specifically, I guessed that it was probably keeping track of ability usage per stroke, not per hole, which it turns out was a correct guess.
First of all, bring Astrid as your caddy, and in my experience make sure she's equipped with the 75% lucky drop perk and the slow shot bar speed perk (precise putting power is important here).
The setup is pretty much what Elem3ntal80 and TheBigBB came up with; plop the ball on the right side of the green of the first par 3 on Rocky Ridge. I found that somewhere between 80ft and 86ft worked for me, smack dab in the middle of the right side of the green. If the ball doesn't land in the middle, putt it over towards the middle, such that the putt does not put you materially closer to the hole.
Once you have the ball positioned, make an eyeball estimate. I usually added about 4 feet from the hole to the distance and adjusted horizontally somewhat to the right (I never had to add more than one grid box, usually small fractions of a grid box). Now, check your work using Astrid's caddy ability. Once you've started to figure out how this general putt breaks, usually you're pretty close and the adjustment necessary is a matter of in game inches to the right or left. Make these projected adjustments and note the final distance and left/right positioning for future reference.
Now here's the trick: don't take this putt. Or rather, make sure this putt goes nowhere. I found the easiest way to do this was to let the putting shot indicator go all the way out and come back, then just as it's within millimeters where the shot indicator started, click A. This should result in a putt that barely moves. This can take some practice but remember, if you hit the button too late, nothing happens at all and you can try again. Once the "nothingputt" has been taken, you shouldn't be any closer than a foot or so from where you started, and more importantly the NEXT putt will be made without the use of the caddy ability, despite already pretty much knowing almost exactly what you have to do based on having used it for the prior stroke. As such, redo the projected adjustments you got based on Astrid's ability and let it rip. Once you sink the putt following the nothingputt the achievement should pop.
I found it only took between 15 and 20 tries to get this achievement including the experimentation so this might be a faster way for some to get this.