The first trial. You will need food, production, and authority. The game will notify you of this 5 turns in advance on turn 27.
The trial itself starts on turn 32.

The Sanctuary of the Falcon takes 15 turns to build and 6 production per turn without using anything to speed it up. You have 10 turns to complete it for a bronze medal.
You can speed up production by spending 10 food or 10 production, each giving one turn faster construction.
On turn 33, the cult of Horus-the-hunter turns into Horus-the-ruler, and you get one free activation. This cult will reduce the time taken to construct your current building by 2 turns.

Gold victory is achieved if you complete construction before turn 34 and gives a one-time bonus of 30 food and 40 production.
Silver victory is achieved if you complete construction before turn 37 and gives a one-time bonus of 10 food and 20 production.
Bronze victory is achieved if you complete construction before turn 42 and gives no extra reward.
If you fail to construct the sanctuary, you will not get its reward of +1 authority to the tile it is on, and a low morale event for 6 turns, which reduces your authority income by 1 per turn.

Exodus from the Sahara is your second trial. You will be notified of it on turn 56, and it will start on turn 61.
You will need food and population limit for this trial.

The trial has you reducing social tension to 0. It starts at 75 and rises by 5 every turn you pass. it also sets your unrest to 20%. If unrest reaches 100, you will fail the trial, giving you -10 culture and -3 anarchy per turn for 3 turns.

You reduce tension by spending food, expelling a worker, or reforming society(once)
Spending food removes 15 tension and costs 40 food per turn, going down every turn you pass(More the first few turns). It also reduces unrest by 5%
Expelling a worker removes 15 tension and costs you one worker. It also increases unrest by 10%
Reforming society reduces unrest by 20%, and raises your population limit by 2. It will cost you 20 authority to do.

A gold victory is achieved by reaching 0 tension before turn 63 and it gives a one-time bonus of 160 culture and 40 authority
A silver victory is achieved by reaching 0 tension before turn 66 and it gives a one-time bonus of 80 culture and 20 authority
A bronce victory is achieved by reaching 0 tension before turn 71 and it gives no bonus
Failing to achieve victory gives you anarchy for 3 turns, giving you -10 culture and -3 anarchy per turn.

This trial comes with events. I've not tested much, but here is the list of what I've found:
Turn 62, 2 areas get damaged.
Turn 63, permanent loss of 2 food and 2 production per turn*
Turn 64, 2 free workers, two more areas damaged
Turn 65, 2 areas get damaged
Turn 66, 2 areas get damaged, +1 population limit
Turn 67, 2 free workers
Turn 68, 2 areas get damaged*
Turn 69, 2 free workers
*Event happens even when trial is already resolved at this point

Note- The achievement "Hospitable host" requires you to complete it on the first turn.

The trial of the Hierakonpolis Chiefdom is the third trial you will face. You will be given advance notice on turn 82 and the trial starts at turn 87. You will need food, production, and soldiers.

In this trial you need to unite 6 tribes through gifts of food and production, or military might. The cost to unite peacefully will go up every time you do it, but they start at 30 food and 30 production.

For a gold victory, pass the trial before turn 89. You will gain a bonus 2 authority growth. Your home region on the Egypt map will improve by 1 food and 2 production.
For a silver victory, pass the trial before turn 92. You will gain a bonus 2 authority growth.Your home region on the Egypt map will improve by 1 food and 2 production.
For a bronze victory, pass the trial before turn 96. Your home region on the Egypt map will improve by 1 food and 2 production.
Failing the trial will cost you 197 authority(Not tested for variables or difficulty)

The Great Drought is the fourth trial you will encounter, being notified of it on turn 116 and starting on turn 121
You will need food, production, and authority for it.

When the trial starts, you will lose 1% of every resource every turn, this is the drought effect and grows as the event continues.
The goal is to strengthen Horus to beat Seth by spending food and authority to increase Horus' strength, and production to lower Seth's strength. The cost of these actions will decrease over time, but they start at 80 for food and production, and 40 for authority. Using one increases the price for that action.

For a gold victory, complete the trial by turn 123. You will get a 20% bonus to production speed per turn.
For a silver victory complete the trial by turn 126. You will get a 10% bonus to production speed per turn.
For a bronze victory, complete the trial by turn 131. You get no additional rewards.

If you complete the trial, you will get the drought effect removed as well as a one-time bonus of 50% culture growth.
If you fail to complete the trial, your population limit is reduced by 3. You still get the one-time culture bonus


This trial includes events
Turn 122 -2 food per turn
Turn 123 -1 food per turn to cattle breeding and flax farms
Turn 124 Building costs for Multi-story houses, Cemetary of the commons, and Painted Tomb -30%.
Turn 125 -1 production in all tiles adjacent to the desert and cities of Egypt
Turn 126 -2 food per turn
Turn 128 -2 food per turn

The fifth trial is The Ombos Invasion. You will be notified of the event on turn 146, and it will start on turn 151. You will need production, soldiers, and authority for this one.
Note that this trial will be skipped entirely if you defeated the Ombos before turn 151.

This works similar to a normal attack, but with three options to influence it.
Spending authority will reduce their army by 10% for 25 authority, costing more every time you use it. There is a limit to how much you can do this.
Strengthening your own troops gives you soldiers, 60 soldiers for 50 production, with the cost rising every time it is used.
The third option allows you to start the battle early.

For a gold victory, start the battle before turn 154 and win it. You will gain +30 soldiers per turn.
For a silver victory, start the battle before turn 157 and win it. You will gain +15 soldiers per turn.
For a bronze victory, win the battle. If you do not start it early it will trigger on turn 161.
If you lose the battle, you lose 15 workers and 6 areas become damaged.

Almost done! The Civil War is the 6th trial, you are notified of it at turn 176 and it will start on turn 181. You will need production, soldiers, and authority for it.
Note that this entire trial will be skipped if you have not yet united the tribes on the Nile.

When the event starts, almost the entire Nile river will revolt. You get two options to reduce their numbers to something managable through the event. Spending production reduces their numbers by 5%, with the cost going up every time it is used. Authority can be used to reduce their numbers by 5%, with the cost going up every use.
You do not need to immediately take out all the rebels, 6 is enough to pass the trial

For a gold victory, complete the trial before turn 184. You get a one-time bonus of 400 authority
For a silver victory, complete the trial before turn 187. You get a one-time bonus of 200 authority
For a bronze victory, complete the trial before turn 191.
On turn 191, all rebels turn into tribes, gaining much more soldiers and becoming more difficult to take over.

The final trial will start at turn 204, and you are notified of it at turn 199. You will need all resources for this.

You will need to create a unified pantheon, costing 45,000 culture.
You will need to build the city of Memphis, costing 770 production per turn and taking 10 turns. Up to 3 workers can build this at a time. You can not begin construction if you have not yet unified all the Nile tribes.
You will need to celebrate after you've done the other two, costing 5,000 food.
And you get the option to reform society, costing 300 authority and more every time you use it, but every time you do the cost goes up.

For a gold victory, unify Egypt before turn 207
For a silver victory, unify Egypt before turn 214
For a bronze victory, unify Egypt before turn 221
If you do not unify Egypt, you lose. But you can still keep playing if you want to, just like if you win. Not that there is anything to do after this.