I've never had a coach, and I reached about 2000 over-the-board (Canadian Chess Federation rating, which is pretty close to FIDE). That was back before the Internet was a thing, so no Youtube videos.
It took years, though, and I didn't break 1800 until I started teaching at chess clubs.
You must have obviously read books. Op was asking without any lessons or coaches. 2000 rating without a coach is nevertheless good achievement.
You can improve by your own which is theoretically possible with systematic training like Alpha Zero and Leela Zero training but practically impossible.
Training methods,
1. You can start playing random moves 1. a3 or 1. e4 or 1. d4 (for 100 games)----> then reassess which move give you better percentage of winning. If it is 1. e4 (I will choose e4 in next games)
2. Then go further moves by playing (e.g which sicilian variation give you more winning chances, choose that variation)
3. By this way you know the best winning probability in opening.
4. Same technique apply in middle game /endgame (which pattern give you more chance of winning, e.g connected pawns vs isolated pawns etc)
It is scientifically proven that Alpha Zero and Leela Zero are already successful after training millions of games.
But for GM level 500,000 games is probably enough.(already achieved)
For 2000+ rating, 100,000 games is probably enough (assumption)
Wait a sec, could you clarify what you mean by 'lessons'. Does that include books and videos?
The OP is asking how far you can go just by practising and making your own observations about the game. "No coaching/lessons" means no learning from experts. Reading books or watching videos created by masters telling you how you should play the game certainly counts as learning from experts. In other words, what if you play according to your natural talent only, without any studying. The answer is: not very far.
To the OP, I really can't imagine how a person can improve at chess without using any resources. The trial and error method is very impractical to say the very least.
I actually find this OP question quite funny, as it's sort of suggesting that people who study the game seriously are gaining some sort of unfair advantage. Imagine telling someone, "You beat me only because you've been reading Kasparov's books and studying his games. Otherwise you'd be a total patzer and I would've crushed you!!" 
@nyku13 @Rocky64 My question came from wondering how you can know how good or not you really are,as self-evidently,as with anything, some are advantaged by training, their upbringing,when they started, what was available to them etc.(not unfair, just as a fact) Those of us-and I'm sure I'm not the only one-who started early enough (I learned moves at 4)-then basically just played with others who could play, maybe couple times a week in school lunch breaks, plus a few matches a year for the team-fairly typical(at least 45,50 years ago!)-I would imagine, anyway-I think must be at a disadvantage to those who had books, lessons, advice on how to play,as opposed to just learning by experience and observation-not that there was zero input-you knew elementary stuff, like pawns to K4,Q4(get my age?!) develop the minor pieces, avoid the trademark Scholar's Mate, King Queen/Rook mates-but that was about it. I am a bit unusual,I suppose,in that until joining chess,com few months ago,I hadn't played a game against a human for about 40 years-I've played more games in said time than probably in rest of my life(including computer games also)put together. I decided I wanted to see how far I could get before starting, which I intend/intended to,to study-acknowledging, of course, that there was nothing to stop me in past or present,from getting books-(did get one, but never got that much through it ) I in no way was implying anything unfair or even amiss with those who had all resources, people needed to give them the chance they took-let alone all those who to their great credit,put time in to study and progress.
I learned to move the pieces at the age of 4 and only improved 8 years later (with coaching).
Obviously the approach of not studying and just learning by playing won't work well. I started few months back and have studied a lot of tactics and master games which has made me develop faster than I would have without studying.
Study as much as you can then see what your potential is.Even with all the study you cannot be a top player if you don't have the talent. You don't necessarily need to have a coach because there is ton of information available if you invest in the right places.
It's how disciplined you are going to be.There is a ton of quality informational material available and it depends on how you approach it.I believe(just my opinion) that if you have a good approach and are"truly focused" on careful study(books,videos,lessons on this site,game analysis,playing etc.) you can become a good player.How god,depends on how far you take it and of course a little talent,but it's all there waiting for us.....
One problem.....There is so much stuff going on,particularly on this site(a good/fun thing) that it's very easy to get side tracked and not dig into correct and careful study....I am a perfect example of that.
It's how disciplined you are going to be.There is a ton of quality informational material available and it depends on how you approach it.I believe(just my opinion) that if you have a good approach and are"truly focused" on careful study(books,videos,lessons on this site,game analysis,playing etc.) you can become a good player.How god,depends on how far you take it and of course a little talent,but it's all there waiting for us.....
One problem.....There is so much stuff going on,particularly on this site(a good/fun thing) that it's very easy to get side tracked and not dig into correct and careful study....I am a perfect example of that.
I don't mean to be offensive but given that you have solved over 30k tactics I don't think you have the talent for this game
I do tactics at a very quick pace purposely.I'm not worried about the number I do or my particular talent....Thank you very much.
Btw,of course you are trying to be offensive,but no offense taken.
A good rating to achieve without coaches or minimal coaching? I don't think this question can truly be given a straight answer. That's because....it all boils down to the individual playing the game. The bottom line, is that some players brains are just not routed to play chess at a very high level, even with coaches. Not to mention, without coaching, chess can take a lifetime to master. Look at Bobby Fischer, for example. He was a mere 6 years old, and already a chess grandmaster. Everyone's brain is mapped out differently. When we reach our potential, then that's it, there's nothing more to give. If a person has been playing chess for five years straight, and sees no gradual improvement from his 1100ELO to 1200ELO, I think its safe to assume this person has reached their potential. It's not fair to judge this as a good rating or bad rating, its just a rating for that player in general. ( I'd like to also point out that I played my first 25-50 games of chess.com...and didn't even know what the ELO was.) If I had to give an answer to this question, then I would say a good rating would be at least 50 points higher then the average ( which is usually a 1010-1020) Besides, I've gotten to the point where I like the percentile a lot better then the ELO rating...it looks like a much better number 
Look at Bobby Fischer, for example. He was a mere 6 years old, and already a chess grandmaster.
Fischer gained the Grandmaster title at age 15.
only out by 9 years.
Nine years in the OTHER direction would have made him minus-3 years old.
I've never had a coach, and I reached about 2000 over-the-board (Canadian Chess Federation rating, which is pretty close to FIDE). That was back before the Internet was a thing, so no Youtube videos.
It took years, though, and I didn't break 1800 until I started teaching at chess clubs.