First scenario: Indeed, you need to increase your accuracy as much as possible to challenge the Talisman. If they are using Baseships, note that you will have an easier time defeating them because of the penalty to defence of the baseships and their lower speed (they will not be able to stay at range 8 where you cannot hit them).
You may also want to use special weapons, such as the infamous Null Space weaponry, if the Talisman ships are of the worst kind: heavily defended, with Scattering and Stealth Armour, fully trained and staying at maximum range. In such a case, your odds to hit are very low, and you will have to hit several times to break through the armour/shielding. So the Null Space weapon can pierce through armour and shielding, allowing you to target internals. You would have a fairly important chance to bring the Talisman or weapons down with this kind of attacks.
Second scenario: Since both sides are using Talismans, ECM/CS/training only matters for ships that lose their Talisman during the battle, if you believe it may have an influence. I am no expert for designs to use in such a case, as I stay clear from any and all fleet with the Talisman even if I have the Talisman of my own. I don't feel that lucky to challenge them in a game of chance.