I am having trouble doing well on hard missions (level 20). Any tips on which sylesti to use?

The most effective way to do missions is to have pets that specialises in them. Eg, for a strength-based mission, use a pet that has all level and proficiency points put into strength.
Different species do have different base stats for a certain trait. But usually the difference is by a few points so it shouldn't really affect anyway.

Even so, some pets start off with such a low base that even if they are at a high enough level to do the mission (ie level 20 pet for a level 20 mission), they may not have enough stats to succeed the mission.

A rough guide on how much stats is needed to successfully do the mission: http://www.sylestia.com/forums/?t=1029

So if your pets are of that level, but does not have high enough stats, you can either put equipment on them to raise the stats, or just use them for lower missions until they gain enough level points to meet the stats needed.

I use a level 38 on the level 20 missions with high stats, but I still can't complete the missions.

You need to put all the stat points and proficiency points into ONE stat. IE, Agility, and then only use that particular pet for Agility Missions. In the tab that you have for mission pets, it looks like your points are all spread out - that won't work.

Ohhh That makes perfect sense! Thanks!