Take note of the health meter of your crew members. You usually cannot play them more than once due to their injuries. Use Data's healing super power by matching the blue gems early to increase his healing bar. Use it when it becomes available. Although you cannot keep your entire crew at maximum health, you will cut down on the waiting time for them to heal on their own.
Heroes
It is difficult to progress in the single player campaign without additional heroes. Win matches in Versus mode until getting your third hero, then go back to single player mode to progress easier, especially against teams that have two crew members. You will also earn rewards such as card packs and other items in the process.
Matching
Create matches based on your skills and try to take an offensive posture. During crew fights, note the color of the attacking character or the red and green ones during the Starship battles. The higher your characters' levels, the more tiles will result in offensive moves. Keep your crew's special skills in mind. For example, Data has blue tiles, Worf has red tiles, etc. They will increase as you they are upgraded and more special abilities become available. Try to fill them up and use them when they become available. Target the strongest opponent first, even though they have higher health and are more difficult to defeat. However in some situations you may want to consider targeting the lowest health characters first, especially if they have multiple special skills available. Begin by searching for matches that are four pieces or better. Your opponent will not be able to use the special stones created this way. If you get a five piece match, use the created tile with the one you need the most.
Upgrades
Level up your characters and Starship to keep up with the increasing difficulty of single player mode.