Medal Traits are; truthfully, the single most important part of being able to finish high-level quests and end game material. You may have noticed in the past that while your amazing Tier 8, seven star, maximum guilt medal is fantastic at defeating lower level heartless it can't even scratch some of the level 5000 bosses that appear in high score challenges and other events. The reason for this difficulty is most likely that you do not have the medal traits that you need in order to fight effectively. So lets take a look at medal traits, in order of their usefulness to you.
1. Ground Enemy DEF -60%:
This is hands down the best trait that you can get on an attack medal and is absolutely essential for completing high level content. Once you start fighting bosses and heartless; either through events or through the coliseum, that are leveled in the thousands you will notice that no matter how high the strength rating of a medal is it will only do 1 damage per hit if it does not have this trait. That is because the defense rating of those high level enemies balloons so much that the strength rating of your medal can't overcome it. This trait takes that defense value and reduces it by more than half allowing you to continue to do damage against those enemies. I rate this trait higher than Aerial Enemy DEF -60% simply because a larger number of bosses are ground type enemies. ALWAYS KEEP THIS TRAIT!
2.Aerial Enemy DEF -60%
The same rational for the ranking of Ground Enemy DEF -60% applies here. ALWAYS KEEP THIS TRAIT!
3. Extra Attack: 40% Power:
Naturally more attacks are better so this trait will always be useful and can help you to pump out a little bit extra damage. However, where it really shines is in support medals where casting it twice will provide twice the buff. A +3 Strength medal will now provide +6 Strength, and so on. ALWAYS KEEP THIS TRAIT!
4. Damage in Raids +40%:
This medal trait is great for defeating raid bosses but is exclusive to that purpose. Unlike Ground/Aerial Enemy DEF -60% it lacks versatility in its use and thereby it isn't rated as high as it would be otherwise. None the less a percentage increase to your damage isn't something to scoff at unless you simply do not like to challenge raids so unless that applies to you this trait should be kept.
5. STR +1000:
You will not see a monstrous improvement to your damage output with this trait like you will the others listed above, but it will still improve your numbers slightly. If you get it keep it but if you get one of the traits listed above don't hesitate to replace this trait with one of those.
6. Max HP +800:
This is the only way to continue to increase your HP past the limit set by avatar boards. While it isn't the most useful trait when it is combined with one of the better Defense Boost Max skills it can allow you to survive hits from raid bosses. With that said when it comes to PvE at some point the damage by all enemies vastly surpasses your HP pool and defense becomes a moot point.
7. DEF +2000:
As above this trait has the potential to reduce the damage to you slightly, but I haven't noticed a significant change when using the trait and ultimately the damage numbers of the enemies you fight will overwhelm your defensive capabilities so focusing on your offence is the way to go.
8. Max Gauges +2:
This trait is only really useful to new players who don't have medals that restore gauges yet. Once upon a time there were only a few gauge restoring medals that not many people had so this trait was very valuable. However with all of the Damage Boost Max + 0/1/2 Gauge skills and the gauge restoring medals that we have now this trait has lost its usefulness.
9. Poison/Paralysis/Sleep Resist 20%:
The only time that this trait is useful is when fighting an enemy that gets to attack before you and they have the potential to inflict one of these status effects. That said, if your spirit is sufficiently leveled it will gain the ability to cure you of any status effects once per battle which nullifies the usefulness of the trait entirely. There is some small potential that the trait could be useful in PvP, but I have not seen many players that choose to use status effect skills over damage and defense boosts.