Start by spending your money in the shop. The boost you get from the powerups are enormous, and lets you conquer more levels. Once done, upgrade all characters to level 1, this will keep them alive. The level bonuses stays even if it's not your main character.
You can use powerups at the beginning of any battle, and those will last and any next battles on the same playthrough. Use them well.
Every enemy you kill gives you 2 exp points for your main character. Those "exp points" lower the price of the next upgrade by the same amount of gems. So play with the characters you want to level.
Keep away from rats as they always try to suicide in the middle of your train.
Never form a long train in line. Try moving often so enemies have to face many characters of your team at once. This also prevent them from killing the people at the center of your train.