Gems of War

TLDR; stack up keys, use them to get featured-troop tokens. **NOTE** Some weeks don't have a featured-troop, and will not get the bonuses noted below. Check the odds before opening your keys and verify the featured troop.

I wanted to share my math on this to help people plan their attack. There are two ways to go about this. The pay to earn the achievement method and the free-to-play method.

The pay to earn method is easy enough to understand. Buy the $10 (or regional equivalent, I'm sure) headstart pack every week for 5 weeks. This gives +5 tokens for the featured troop of the week, immediately getting it to Level 1 shiny and 1/3 of the way to Level 2. Then you only need 10 more. Of those 10, 5 can be guaranteed-earned by completing the stages of the weekly event. Now you only need to pull 5 randomly from keys. The featured troop also has a 20% chance of appearing in any chest opened that week with shiny keys. And you can get multiples per pull (1, 2 or 3 with decreasing odds).

Percentages from the devs:

Non-featured
1x 0.50
2x 0.20
3x 0.10

Featured
1x 0.10
2x 0.07
3x 0.03

As always with pure random with no pity timers, there's no guarantee as to how many chests you'll need to open to get your last 5 tokens. It could be as few as two chests, but on average you'll need 15-16 keys to round out the weekly troop in the given week.

You can buy some more keys with the Heroic booster and get up to 15 keys per week. 15 keys gets you 4.95 featured troop shiny tokens, on average. This gives you a really good chance (though still slightly below 50%) of getting it in that week, each week you buy both $10 booster packs. Doing this for 5 weeks ($100 total) probably gets you the achievement. If not, a few spare weeks after if you missed it almost certainly does. This is definitely the most efficient path to earning the achievement. You are also maximizing the increase in power to the currently limited, but soon to grow pool of shiny troops available, so you are paying for some small advantages, though to mostly irrelevant troops.

However, if spending $100+ to earn a single achievement doesn't sound good to you, this is possible with a F2P method. It just takes a long time.

F2P only gets the 5 guaranteed tokens for the featured troop from the events, so you need to randomly pull 10 tokens from shiny keys now. With the same randomness caveat as above, that's 30-31 keys on average. F2P also gets fewer keys, getting only 7 from the event full clear.

It's worth noting here that not every week has shiny keys in the guild event rewards. Since the release of this content it has been 4 weeks on, then 1 week off. Guild events that reward the shiny keys include: Journey, Raid Boss, Invasion (Siege Towers), and Tower of Doom. Generic weekly events where you choose from 1 of 5 battles may not have a featured new captain, and therefore won't have a featured troop of the week to try to accelerate, and the events don't give shiny keys. Though you only need to hit Reward Level 12 instead of Reward Level 16, so it's a nice respite from the grind, I guess.

After 5 weeks of guild events giving you shiny keys, assuming your guild hits max rewards, you'll have 35 keys, which is a pretty good chance at earning the necessary tokens for the featured troop of the week. Spending 35 keys gives you 5 (free from rewards path) + 11.55 on average = 16.55 on average. Repeat x5, and it's 25 weeks on average, saving up keys in between, to earn this achievement. If you just go every 5 earned weeks like this, you're going to end up with a better than a coin flip five times in a row for the achievement.

To maximize your luck (or more accurately, to minimize your unluckiness) I'd recommend holding keys until you have an even larger number than the ~31 necessary, on average. This way if you catch an unlucky break, you can at least have a much higher chance of ensuring you capture your 1/5 achievement progress each time. Either way your progress is slowed, but at least in this case you're have progress to show for it.

Something on the order of 60-70 keys, giving nearly 20 tokens for the featured troop on their own, in addition to the five guaranteed, should be enough even for unlucky folks, and I count myself in their number, to get their +10 for the weekly featured troop.

Get to 15 shiny tokens for the featured troop--then stop! The keys you save start the rebuilding process faster. Rebuild back to your comfort level and try again. This process still averages 25 weeks, but practically this method takes a bit longer as you'll have a few weeks of buffer still left at the end, or have consumed a few extra weeks worth from bad luck.

This method should work until they update the featured troop mechanic, reduce rewards, or otherwise mess about with the system. It is NOT affected by the increasing pool of troops that can become shiny. Hitting Level 2 with non-featured troops is possible, but not required for this method. It would speed up the F2P process if you're really lucky. But the odds are incredibly low, and they're only going to get lower.

If you use all 7 keys each week and rely on hitting level 2 on the base pool, it'll take 56 weeks on average, and that doesn't include the fact that the pool is going to grow. Even collecting 5 free for the new troop each week means the pool to hit level 2 is growing by 10 each week, while 7 keys nets 10.71 tokens on average from F2P. So you'll be making 0.71 token/week actual progress, without additional assistance from special events, or, of course, purchases, which takes us back to the top.

Updates: A complex way to get more shiny keys has been provided. The return is very poor, but it does not cost money. It does, however, require you to grind PVP for a long time, and the worse your attack teams, the longer you'll have to grind. Some math on that follows in a spoiler for those who want to know about it.