Arenas: If you are low on gems, gold, or food and get to the point when you can't afford to skip and are too weak to fight them, use weaker dragons who are NOT on your battle team. (Note: You WILL still lose trophies and it will take up one battle charge.) Then another tip: Look at the enemy dragons' elements and group (Vampire, Titan, Legend) first. Then the rank, rarity, and the empowerment. Do them one by one. Compare those to your dragon team. If you are too weak to fight, press the "Skip" button. It might slow you down, but it'll help you win the battles and take on challenges.
Leagues: In the League battles, the dragons are surprises until you fight. So here is a tip that SOMETIMES works in lower-level leagues (1-20): Look at the enemy's icon. If it is a weaker or common dragon, your chances are it'll be a stronger team. It is the opposite with higher ranked or stronger icon dragons. (This usually does NOT apply if you are level 30 or above, or if you have a Heroic.)
Quests: The first several Quest Battles are easy, as they put no-ranked common-very rare low level dragons in those battles. Those battles are a good place to give recently-hatched dragons a rank.
Other tips: If your dragon's defending element is an Ancient World element, there are upsides and downsides. Upside: No dragons have strong attacks against you. Downside: It doesn't have strong attacks and often does not deal as much damage as other attacks. You're basically better off without using them, just having them as defending elements. Titans always have a shield, so you should use a dragon you are not saving to disable the shield. To see enemy or your dragons' rank, elements, and empowerment while fighting a different dragon, you click on their face in the frame to see that info. Remember to try to have most elements spread out on your team for strong attacks. And finally, here is a battle strengths chart:
Now please try to remember this for next time you battle! Bye! 
