Fighting: The Artificial Intelligence in Dink Smallwood isn’t really that good, so you can easily keep running around and blasting your enemies with fireballs (and later with Hellfire). If you build up your magic early, this is a really good tactic.
Nothing beats killing enemies with a sword though, so be sure to buy new ones whenever they become available. The hit-and-retreat tactic works best here: you hit your enemy, run back, hit him again, run away and repeat. Try to make the enemy run into your punches and slashes, otherwise he might touch you. Remember, practice makes perfect.
The original bow isn’t quite that powerful weapon, but luckily the Massive bow is and the Fire bow (on the Duck Island, check the walkthrough for a precise location) is even one of the strongest weapons in the game. Learning Bow Lore is a must though, it will greatly increase the amount of damage your bows can do.
Bombs aren’t that useful, they’re too slow to be really effective. Don’t let that stop you from using them though, if it pleases you.
There are tons of secret goldens hearts, potions and chests to be found in the Dink world, so explore the map carefully. Burning down trees with the fireball can sometimes reveal a secret entrance, so try to always do that. Rushing through the game either isn’t recommended, try to level up as much as possible.
Stock up on elixers, you’ll need them for the final battle. If you can’t buy elixers yet, take as much alk nuts as you can with you. They don’t give you that much health, but it’s better than nothing, and above all, they’re free.
Lastly, save a lot, you never know when you’ll die.