There are a total of 48 Secondary Objectives in the game. Most of these Objectives are simple kill everything in a certain area/camp and kill a certain amount of enemys.
Most of them don´t show at the start of a chapter so if you run in all corners of a map befor heading to the main objective should do the job finding the most of them.
Simple but a little bit missable are "Rescue Armys Missions"
This secondary Objectives are popping up if you are near this armys. Only problem is that those guys don´t last that long so if you see missions like that help them immediatly ignoring anything else until Objective complete pops up.
A little more trickier are those who need you to kill enemys in a duel in certain time mostly between 90 and 120 seconds. On easy difficulty triggering Fury with B should to the job and attacking with Y with all characters or in Paris or Odysseus Missions with there overkill attack XXXY (unlocked by an item early available).
The only ones I missed during the game was the first time I played with the Amazon Queen. There are a total of 4 secondary objectives in this chapter and if you simple follow the standard road you will only be able to get 2 of them all the time no matter what you do.
At the start of the level get rid of the first group of greeks then you`ll see an grassy side path on the right which leads to the back of the mansion.
If you approach the back gates there is an Guardian who wants to be defeated for 2nd Objective #1 then free the Amazon Handmaidens at the small house for #2 then head straight to the main gates and support an allies army before they are deated for #3 and at last secure the front of the palace to get #4.
An another actually not missable but very annoying is in Ajax last chapter called "Madness" It demands that you reach an Hero without getting hit which is not that easy because he has no range attacks and there are lots and lots of enemys. After trying multiple times legally I found only one option: Just rush through. But you can´t just simply walk/roll through the enemys they will attack you and they will hit you if you don´t watch out.
I rushed from the start ignoring everything doing this:
1st group evade going left
2nd group rolling straight through the middle
3rd group shouldn`t be able to spawn in time if your fast enough
4th and 5th group they`re running straight at you covering the whole path so I approached from the left and rolled in zig zag movements right through them.
There is a bit of luck needed. If you fail just reload the checkpoint before going to the Hero. If you have no luck at all just play the challenges on normal there is an item what makes you invulnerable during the evasion roll and with this you can easily do this.
Another in some way hard to achieve item is fighting against Hektor with Partrokolos on Expert without getting hit. If your not to good in counter and evading the pillars of Apollo I vouch for this item combination.
Amazonian Royal Sash / Hephaistos Armor / Jasons Bracers, Banner of Troy, Quick Attacks Max, Fury bar max, Sword of Aristea (Fury damage plus) . With this combination you can beat Hektor easily without getting hit.