I'm always looking for friends for events like the Lottery or Pinatas =) 
I really like the Ascent of Olympus gamemode and I'm up for any questions. Here is some data I've collected and a strategy I came up with, as it works for me:

Olymp - tips and data

Disclaimer: The strategy is not a "joker" you can use in any situation. There are situations where it's much better to NOT follow the strategy stated here. These are just some notes on what I found out is working well for me to Ascend the Olympus. 

All pictures are property of UBISOFT
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Strategy Summary and general tips
I'm working towards a goal of what cards I want to have at the end of each Threshold. 
These are:

End of Threshold 1: at least three 3*+  cards leveled at least 3/3*, 3/3* and 2/3*
End of Threshold 2: at least two 4*+ cards leveled at least 4/4* and 3/4* (achieving this in room 3-1-0 also is absolutely fine - make sure you pass the 11/11/11 requirements in room 2-1-6!)
End of Threshold 3: a 5/5* card additional to two 4/4* cards

It's not perfectly easy to obtain these cards at that point in the run. There are many times you'll end up with no 5* cards at all. It's better to use three 4* cards or even just two 4* cards and a 3* card instead of forcing to get this 5* card. 
These calculations are about winning in the final room, but don't forget you'll have to get there first! If you lose on the way due to trying to build the "perfect team" you'll "lose" more fragments than if you were just going with a semi-perfect team.

General tips:
Take the hardest path. The rooms seem to be slightly more difficult but usually it's possible to get the 100% for better rewards (details on rewards on the next text box). Several times it's the option to take a better horse early on. 
(earliest: 4* horse in room 1-2-5, 5* horse in room 2-2-2) This helps you to be able to level them soon enough to be ready for threshold 3 and the final boss.
drachma
Facts (numbers, calculations and rewards I've seen)
Requirements
on the hardest and fragment paths: 
Threshold 1:
1-1-0 (green): 1x 1
1-1-1 (green): 1x 2
1-2-2 (orange): 2x 3
1-1-3 (orange): 2x 3
1-2-4 (orange): 2x 4
1-2-5 (red): 3x 6
1-1-6 (red): 3x 7

Threshold 2:
2-1-0 (green): 1x 5
2-2-1 (green): 1x 6
2-2-2 (red): 3x 8
2-1-3 (red): 3x 9
2-2-4 (orange): 2x 9
2-2-5 (red): 3x 10
2-1-6 (red): 3x 11

Threshold 3:
3-1-0 (green) 1x 9
3-2-1 (red): 3x 11
3-1-2 (red): 3x 12

3-1-3 (orange): 2x 12 (the only difference between the middle and the right path)
3-2-3 (red): 3x 13

3-[1/2]-4 (red): 3x 13
3-[1/2] 5 (red): 3x 14
3-1-6 (red): 3x 15

Boss: 4x 18

Sum of starting skills and with max lv-ups:
2*: 5 + 4 = 9
3*: 7 + 8 = 15
4*: 9 + 12 = 21
5*: 11 + 16 = 27

Skills needed to defeat the boss:
18+18+18+18 = 72
(to get 100% you'd need 2 5* cards and 1 4* card, all maxxed)

Rewards
I've seen: (from most occurance to very rare)
Threshold 1:
Green rooms: 
Booster +6, 2* horses, 1 level for 1 horse, 2 energy 
Orange rooms:
3* horses, 1 level for 1 horse, 2 energy, 2* horses, booster (+8, +6, +4)
Red rooms: 
3* horses, 1 level for 1 horse, booster +8, 1 level for 2 horses, 4 energy, 2 energy, 4* horses, booster +4

Threshold 2:
Green rooms:
3* horses, 1 level for 2 horses, booster +8, 4 energy, 2 energy, booster +6
Orange rooms:
4* horses, 1 level for 2 horses, 4 energy, booster +8, booster +6
Red rooms: 
4* horses, 2 level (any), 4 energy, booster +10, 6 energy, 5* horses, booster +6

Threshold 3: 
Green room:
4* horse, 2 level, 4 energy, booster +10, 6 energy, booster +8
Orange rooms:
booster +10, 4* horse, 2 level, 6 energy, 5* horse, 4 energy, booster +8
Red rooms:
booster +10, 5* horse, 2 level, 6 energy, booster +8
drachma
A little more detailed
Note: I try to avoid taking boosters. They "have" one energy while even a 2* horse can help at least twice, usually. There are situations where a booster is quite helpful. But usually it's safer (at least it was for me) to use the horse cards.
During Threshold 1 I focus on building a decent team of three (to four, if it fits) 3*+ cards. 
We start with a team of 3*/2*/2* (at least).
In the beginning I focus on:
* taking new cards if they provide more in a weakness of my team than the levels that I find. (If my team has 0 1 and 0 in red I will even take a 2* horse with 2 in red instead of 1 level)
* taking new 3*+ cards (if I don't have 3 already or don't need any of the other provided options)
* leveling cards (highest cards first)
Note: I suggest using two 2* cards instead of one 3* card most of the time (unless they are leveled and/or I'm low on cards) as they will be useful up to room 2-2-1, but usually not that much after that room. We can just use their energy.

Threshold 2:
Here the main objective is to get two 4* cards (or higher) which complement each other (not two cards starting with 4 in red).
The leveled 3* cards can carry us up to 11/11/11 (last room of threshold 2, and second in threshold 3). After that we need to have higher cards. 
While going for 4* cards we need to have an eye on our energy though. Sometimes focusing on energy will be more important than taking the levels, if we wouldn't get 100% in the next room otherwise. 

Threshold 3:
If we are okay on energy and fine on levels, we can take a 5* horse. We may take it as well if our team is lacking some particular skill which the 5* horse can help with.
There are runs where we had to take a third 4* card in room 3-1-0. If this is the case and we are lacking some levels anyway, between 2 levels and a 5* card, I'd suggest taking the levels.
Keep in mind that you have to level the card for it to become useful. A 4* card without any levels is as strong as a leveled 2* card. A 5* card without any levels is as strong as a leveled 3* card. 
Threshold three is very strict with what you need - if you take a 5* horse you will need at least 2 rooms to level it. Most likely you will also need some energy during that time => you need at least 3 rooms before the boss just to level this one card. If you still have to level some 4* cards as well, you will need to find some levels for them too. All of this takes "time" and "time" (rooms with loot) is very rare in the end. 
So, if you're already low on levels but maybe had to take another 4* card I'd suggest just to level the 4* cards and to check if you can take a booster for the final room.