Minecraft: Xbox 360 Edition

This can easily be obtained in the tutorial. However if you choose to make other potions or do this in another world you will need a blaze rod and three cobblestone to create a brewing stand.

Collect sand to make at least 3 glass bottles in a furnace. Then collect nether warts in the nether. Now kill spiders for the eyes and then cook them, kill blazes for rods and turn to powder, kill magma cubes for magma cream, kill creepers for gun powder (use a bow for an achievement), optional mine glowstone or kill witches/blazes for glowstone dust or mine red stone for the dust.

Now fill your bottles with water and in the brewing stand menu place the bottle(s) in the stand for each potion you want to create.

Now place a nether wart and then a magma cream on top of the brewing stand for a potion of fire resistance (It's optional but add red stone dust to extend the duration) which is needed for

After that the next potion you want is a nether wart and blaze powder for a potion of strength. Optionally you can add red stone dust to extend the duration or add glowstone dust to make it more potent. Either ones fine depending on what tier sword you use but aids

The last potion you will want is a fermented spider eye which gives you a potion of weakness. Then add gun powder to it to make a splash potion of weakness, which is a potion you throw, and again you can add red stone if you choose to extend the duration but is needed along with a golden apple for

Any one of these potions will do for
Most likely though this will be obtained in the tutorial seeing as how it's close by and provides a brewing stand and the ingredients for a potion of fire resistance instead of having to travel to the nether and back.

Easy! Load up the tutorial world and head to the potion making section. Get the vials and ingredients out of the box. Fill the vial with water from the pots and place in the Brewing Station. Place the nether wart at the top and once the potion has finished brewing take it from the station and done!

This can be done in the tutorial world.
Just find the booth with the empty bottles on the signs and you will be given a tutorial and ingredients for a fire resist potion. just follow the instructions and your'e set!

*UPDATED*

You can do this on the tutorial world. Find the booth with the empty bottles and sign and you're good.



***

Several resources are required to craft the needed materials to complete a brew.

Sand needs to be fired in a furnace into glass, which then needs to be turned into glass bottles - specifically nine blocks of sand which will be enough for three bottles. Fill one of these with water for the first slot of the brewing stand.

Next, a trip to the Nether will be required to find a fortress so a blaze can be farmed for a blaze rod. This rod combined with three cobblestone will make your brewing stand.

Lastly a brewing agent is necessary - for the purposes of getting the achievement it can be any of the four: glowstone dust, redstone dust, nether wart, or fermented spider-eye. Place the three bottles on the bottom and the agent on top to finish your brew.