Make sure to _RUN_ while you are doing a hit and run.
I have been describing the Eldar to other players as "really fast soap bubbles armed with bludgeons".
Always remember that each battery shot they get against you has 50% to kill an escort, and 25% chance to crit a cruiser. Last night a single shot brought down my eclipse's holofield, forcing a disengage.
Squads of escorts can zoom in and launch devastating strikes against ships almost at will. Be sure not to get too close, or an explosion crit will take out these escorts when the target dies.
When you have finished shooting phase, examine the board for the safe area. This is the place that your ships can sit and have the least chance of taking fire. Look for areas behind terrain, far from the enemy, etc. It is vital to know where the enemy can end their movement, as he will have to move before he can fire. Sometimes the safe area is in an asteroid field, but remember the risks. Also remember that escorts automatically get a re-roll if failing a asteroid check.
Torpedoes are good weapons. They may be equally as effective as battlefield manipulators. A wave of incoming torpedo markers at the enemy line may cause them to split in 2 or more groups. Because Eldar are so fast, you can then choose one of these groups to hit with your entire fleet. If you hit hard enough you may destroy that segment before it can shoot back. This will leave you with your entire fleet, and him with 1/2 to 2/3 of his. And the game goes on.
Pat Estes