MarekVit posted an excellent solution and give you most of the information you need. My solution just should give you an idea how long it can take to unlock the achievement and add some other things. Let's start: The real problem are not the 350k souls you need, because they can be farmed. The 4000 diamonds need a long time to be collected.
You have 5 options to collect these diamonds:
1. Beat bosses in the Drifting Sands dungeon. You unlock the dungeon at the end of the quest line. You can beat 3 booses each day for 20 diamonds total. The troops/bosses have level 20, 30 and 40. That means you need a pretty strong team to be able to beat all 3.
2. You can trade in 50 gems for 20 diamonds once per day in the dungeon.
3. Soulforge level 8 give you the option to craft 10 diamonds for 1000 shards.
4. Guild tasks can give you shards and diamonds. You need an active guild to fullfill the tasks.
5. Buy the daily deal at the dungeon for real money to speed things up, but that's going to be expensive.
At the moment all players receive a daily "welcome to the new update" reward message for six days with 200 diamonds per message. That's 1.200 gifted diamonds total, but i guess players in the future don't get these diamonds.
Sunday is the "diamond day" of the week, because at this day you can earn 70 diamonds for the boss fights and you get 80 diamonds for 50 gems. The daily deal gives you 150 diamonds and 1000 shards for 4.99 $/€.Glitches:
It seems the daily deal can be purchased more than a single time, until you leave the purchase screen. If you leave the screen and reenter a red message appear and says you already bought the daily deal. So until this is fixed you could buy all 4000 diamonds for 150$/€ with the daily deal at a sunday.
Now let's start with the calculation. I hope i don't confuse you too much.
1 day / daily:
20 diamonds for boss fights + 20 more for 50 gems = 40 diamonds
400 shards for boss fights + 400 more for 50 gems = 800 shards
7 days / weekly:
140 diamonds for boss fights + 140 more for 350 gems = 280 diamonds
2800 shards for boss fights + 2800 more for 350 gems = 5600 shards = 50 diamonds
extra diamonds on sunday: + 50 for boss fights + 60 for 50 gems= 110 diamonds
= 440 diamonds in 7 days.
30 days / monthly:
600 boss diamonds + 600 more for gems = 1200 diamonds
12000 shards for boss fights + 12000 more for 1500 gems = 24000 shards = 240 diamonds
x 4 sunday reward: 200 extra diamonds + 240 diamonds = 440 diamonds
= 1880 diamonds in 30 days.
== around 62 diamonds per day (62,66)=== 64 days without the help of your guild and without spending money
Here you see all the new guild task rewards:http://community.gemsofwar.com/t/3-1-guild-task-rewards-pend...
The shard and diamond rewards can cut off some time.
with 12.000 monthly shards (120 diamonds) from guild tasks:
= 2000 diamonds in 30 days
== around 66 diamonds per day (66,66)
=== 60 days (4000)
For the people with a very active guild and the weekly 150 diamond task reward:
= 2600 diamonds in 30 days
== around 86 diamonds per day (86,66)
=== 47 days (4073)
To come to a result: You need at least 2 months and the shards from the guild only saves you 4 days. The diamonds for the guild tasks could save you nearly 2 weeks, but i think most of us don't have the luck to earn the full guild diamond reward each week. However: You can try to work together to complete at least some of the diamond tasks.
Some extra info about the cost for the guild tasks:
Your guild needs 3.660.000 gold each week for all the shards. That's 122.000 for each member with a full 30 member guild or 244.000 gold for 15 members.
For the 25 diamonds task your guild need 1.860.000 gold. All 6 for 150 diamonds requires 11.160.000 gold and that's 372.000 gold for 30 members or 744.000 for 15 members.
The blue statue gives each member 140 gems on the way to the shards and that's helpful to pay the 50 gems each day. Of course you still have to earn 210 gems yourself for 350 each week. There are differents way to collect gems. Completing events, opening chests, collecting kingdom tributes, playing the chest mini game and so on.
That's all i have to add for now. This is a "work in progress" solution. I'll add more/new information later. Especially if i found new ways to earn diamonds. Feel free to leave a comment if you have a question and i do my best to help.