This is what I came across in one of the forums.

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Tactic - no loses, no casualties, no rewinds
Strategist - no battle lose(you can lose hero, win battle and revive), no rewinds
Explorer - >1000% explored total
Cartographer - map all provinces(slinger guards are good for this)
Builder - build ~120 buildings in castle
DragonSlayer - clear 10 sites with "Dragons"
Pillager - get 1000 gold from pillaging
Collector - equip set from 4+ items
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What do you mean by >1000% explored total.

Does it mean you have to have 10 provinces that is 100% explored.
Because in one map, I have a total of more than 1000% explored but I didn't receive the reward.
But I don't have 10 provinces with 100% explored. Some are 80%. Some are 70% etc.....

Game sums amount of % explored by your heroes.
Each province has initial % of exploring, from 10 to 50.
So, safe bet would be around 15-20 provinces with 100% explored.

Here is a question: How much are these rewards worth?

I think it depends on the shard size, but it would be nice to know so that I can start calculating my score.

Tactic
Fame: 200 * (X - 2) / 8

Strategist
Fame 100 * (X - 2) / 8

Explorer
Fame 30

Cartographer
Fame 40 * (X - 2) / 8

Builder
Fame 25

Dragonslayer
Fame 40

Pillager
Fame 25

Collector
Fame 20

There is one for beating Orca on arena (10 battles in hardest league, then with him for title), don't have amount on hands.

X-from shard.var.

After many scum saves I got this one! Granted, since I was playing the first shard (tiny) on the Beginner Campaign, this amounted to about 100 x 0.5 (time) x 0.12 (difficulty) = 6 Fame out of a total of 45.

I have not yet decided at what point it is worth it to pursue the Tactician reward and having to play very cautiously, or sacrificing some units early in the game to get a boost at a key point and then never having to worry about having to protect the low level units again.

The first shard was also a Warrior Start. The second shard is Scout Start and I am finding it to be much easier to keep everybody alive. I think the reasons include only two units for the healer to keep alive and ranged damage that has more than 10 hit points.

Addit: I just found out that attacking Spiders with a Warrior and 2 Swordsman and a Healer is a bad idea and it it has been 20 Turns since the last Scum Save.

1. This award is for goodies, mostly. Give some defence medals to swordsmen and they become immune to T1 units.
Scout will kill T2,3,4 units (they are rarely in big amounts), swordsmen will protect scout and healer from melee. Cast wind shield/stone skin on healer, and you can take on centaurs and nomads.
With this tactic really hard to loose units.
2. In campaign difficulty of rings around demesne artificially lowered. First 10-15 shards you sometimes can't encounter tier 2 units at all. When you play single, you will have T2 unit(s) in third ring.

The reward for Arena Champion is 50 points. I find it easiest with a lvl 30 warrior with sword of blood or rings of vampire and high level defensive gear (your def and ranged def at least above 16 and res above 12) Also needed is the cloak of the phoenix for poison immunity and a floating or flying item. Tip... KILL spiders FIRST!!

PS. To Gremlion.. Thank you for all the quality posts you have contributed. You make the game a lot more fun for me and I'm sure their are other players who have also benefited.