Not really a detailed guide, but here is what it would cost you if you want to just get this out of the way:
You can directly buy this amount by purchasing crystals which at the moment is 50 bucks for almost 7000 crystals. Another 5 bucks gets you 500 so you will have 7500 total.
You can buy 1,250,000 coins for 4500 crystals, 360,000 coins for 1500 crystals, and another 360,000 coins for 1500 crystals which is why I calculated 7500 total crystals.
In a nutshell, it will cost 55 USD to purchase this right off the bat.
Now if you do not want to do this, well, you are in for a grind.
Let's assume a few things here.
First, lets say you get your 5 win streak 3 times a day (which is very hard), this will give a massive gold pack that will average around 20,000 coins each time. Adding in the few silver and bronze boxes you get from your vs match winnings, this adds another 8-10,000 coins a day, which, at best, is netting you 70,000 coins per day, making it a minimum of about 30 days to get this for free.
Here is the caveat, you will probably not reach a 5 win streak unless you upgrade your pins, which is slow and time consuming to do without spending real money, so you are looking at closer to a max of 20,000 coins per day assuming you at least get one 5 win streak. This will bring your total days to 100 to reach this.
Edit: The 5 win streak gold box is different from the one you purchase, so doing the math based on "achievable" coins for free each day nets:
~3,000 for daily win streaks
~500 on average per arena crate, so 10 a day nets about 5,000
Horde twice a day may get you ~1,000
Bounties do not really get you enough so it is negligible. Good for the crystals though.
Free method you will net about 9-10,000 coins per day which equates to 200 days to achieve this. Thanks to bartlannoeye for the correction.
Your best bet might be to drop 5 or 10 dollars if you enjoy the game and buy crystals so you can purchase the bundles. There is a starter bundle for 500 crystals (5 USD) and another bundle for each arena/league you get promoted in for the same price. These contain some epic/legendary pins as well as 5 massive gold boxes, so it may be worth it in the short and long run.
Let me know if you think I should add anything, thanks!