There are 29 different slimes in total, however only 24 of them need to be killed. The other five slimes are from Christmas and Halloween events. The slimes can be found as follows.
Note: Because the Corrupt Slime is only found in a Corruption Hard mode world and the Crimslime is only found in a Crimson Hard mode world, you cannot earn "Gelatin World Tour" with a single world. To avoid missing any of them, have 17 out of 24 slimes before you trigger Hard mode. Then, collect up to 23 out of 24 of the slimes in your original world before travelling to a second world and immediately starting hard mode at that location for the last slime.
The Golden Fishing Rod is a quest reward obtained from the Angler. It will always appear as a reward for your thirtieth Angler quest completion. The Angler is be found asleep in the Ocean biome, either laying in the sand or floating on the water. Talk to him to do his quests and move into an open house. His quest requires you to obtain a special fish that can only be caught while the quest for that fish is active. Each fish has a specific biome it spawns at.
You can get wings before Hardmode by completing a quest from the Angler NPC.
Place any grappling hook into the grappling hook slot in the "Equipment menu". When selected, it will appear on the right-hand side of the screen.
You must reach the upper boundary, where the sky meets space. If you do not have the Wings, Jetpack, or any other means of flight, build a very tall single block tower with regular wooden platforms sticking out of it to use as jumping points. Jump up until you reach the maximum height.
Truffle is an NPC that sells Mushroom-related items such as Mushroom Spear, Hammush, and Autohammer. Get a surface Mushroom Biome with over 100 blocks of Mushroom Grass, Plants, Trees, and a house suitable for NPCs. Truffle will appear very soon afterwards.
The easiest Boss summoning item you can obtain is the Suspicious Looking Eye. It is crafted at a Demon Crimson Altar with six Lenses or can be found in chests in the Cavern.
Fall damage uses the formula: (fall height in blocks - 25) *10. Because that base fall damage number is further modified by your defense from equipment, do not wear any. Dropping from a health of 100 to 10 is enough to earn "Lucky Break". To do this easily, create a new character, dig 34 dirt blocks, then find a flat area and build a vertical tower. Then, walk off the top.
Jumping and flying will not increment your progress. Find a long, straight, and somewhat flat area, then wander around.