This guide ONLY covers the necessary steps to make Baphomet spit out the fifth question. This guide, though helpful in reaching the achievement, IS NOT ABOUT THE ACHIEVEMENT ITSELF. If you want to earn it, just follow this guide and take some more time going to Act I visiting Baphomet a few times to ask him the remaining questions. Simple as that.

This guide is spoiler free (sort of).

This section just explains, in a very quick fashion, what you need to make the "elusive" Fifth Question appear while talking to Baphomet. Once you ask it, you're done, and you can repeatedly visit him in Act I via Act Selection (for example) to get the achievement. Of course, if it is your first playthrough of Pony Island, beating the game is mandatory. It does not matter how many tickets you have collected.

So, it gets down to this:

without exiting the game, meet him once in every Act (any sequence) and ask him a question.

(This was lately confirmed by Daniel Mullins post on Twitter, see the Comments section below.)

That's all. As far as I know, there are no other (major) caveats. If you want some more insight, if you don't know how to get to him or what to do when you encounter him, just go on reading. Otherwise, there's not much more to know (unfortunately, I might add).

Still updating. I will post more images and/or content as soon as I have the time to collect data for the guide. The stuff here should cover all the basics anyway. I am playing Version 1.22 of the game.

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17/01/2017
Daniel Mullins on Twitter confirmed the overall strategy.
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16/01/2017
Sequence was Act II -> Act III -> Act I. Q5 appeared in Act I as reported. So linearity is NOT mandatory. Updating the guide accordingly. The section "The Steps" has been removed since it is not useful anymore, full of redundant data.
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15/01/2017
As hinted by gemberling's playthroughs reported in the comments section below, one could have to make Baphomet ask Question 5 in Act III to earn the achievement afterwards. Though this lies beyond the purpose of this guide, it could be a mandatory requirement to get it, but I cannot be sure of this since on Steam I've earned it already. (This could be false though, since Steam sometimes does not make achievements popup. Just exit the game and scroll the achievement list, it should be there.)

And, it would seem that what I wrote about Q5 only appearing in Act III is false. I'll gather up some data ASAP.
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14/01/2017
Actually it does NOT matter if you write "back" to exit, as long as you DO make a question to Baphomet. Traveling through acts without making questions just leaves them right where they are. So the third caveat (asking him a question) is mandatory.
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13/01/2017: "Where did I die?" is NOT a taboo question in any playthrough. I am beginning to think that the only requisites for Baphomet to lay out all questions are the following:

-- you MUST encounter him in all three Acts;
-- you MUST ask him a question, regardless of which you pick;
-- you MUST NOT exit the game (i.e. "exit to desktop").

Needless to say, this is much easier than I initially thought.
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11/01/2017: "Who killed me" CAN be asked in Act I. Done a playthrough with act jumping with the following steps:

Act I: "Who killed me?"
Act II: "When did I die?"

In Act III "How did I get here?" appeared.

Still have to find out if "Where did I die?" plays a role in NOT giving the fifth question in Act III. Always appeared in Act II until now. It would seem that encountering Baphomet in all three acts is a mandatory requirement for Question 5 to appear.
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Still have to try:
1. a different sequence of encounters (i.e. Act II -> Act III -> Act I) -DONE-
2. jumping to Act III 3 times
3. jumping to Act I 3 times, and then Act II and Act III once

An achievement in Pony Island is named "The Full Truth", which encompasses "knowing every secret from your past". This cannot be done without making Baphomet (I'll talk about him later) all the questions that are needed to reach it.

Merely surfing the Net and lurking Steam did not satisfy me: some say that all of the questions can be made in Act I, some say that you have to travel to Act III to encounter Baphomet for the last time AFTER making all the other questions in Act I. None of these advices worked for me, so I decided to "go out for a quest" (almost literally) and find out The Truth About The Fifth Question.

I call him "Baphomet" because, you know, that's literally the password you have to enter if you want to talk with him. Originally, Baphomet was a pagan god worshipped by Templars, resembling a human with a goat's head. Traces of him can be found as far as the Ancient Egypt and recently he has been used as an image of the Devil. In Pony Island, it is not clear what purpose he might have aside giving you information about your past.

You can meet him in Act I, Act II and Act III.

Act I: at the new Pony Island main screen (in-game), click on the '###########' option and enter the word "baphomet" as password.
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Act II: you have to travel through the whole World Map until you reach the Sin Desert. After beating the level, two new squares will appear, one that leads to the West and the other North. Click on the upper one and follow the (sort of hidden) path until you reach the Cave of Truths.
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Act III: this is a little tricky. The second puzzle game right after you confront Jesus -- that sort of floating angel who shoots purple stars and with two glitched butterflies revolving around him -- shows a glitched flower bush in the bottom right of the screen. Send a butterfly there via the splitting signal and you'll be brought straight to Baphomet.
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Every time you meet him he will show you a vision, and offer to answer a question from a list he gives you. To let him show the vision as soon as you arrive, you can simply type "vision" at the prompt. This goes for Act II and III since in Act I he will do so automatically as soon as you enter the password.

The questions Baphomet might give you are:

1) Who was I?
2) When did I die?
3) Where did I die?
4) Who killed me?
5) How did I get here?

It would seem that, encountering him the first time in any Act from firing up the game, the list of questions is always the same:

"Who was I?"
"When did I die?"
"Who killed me?"

Aside from this, it would appear that Baphomet follows the rules below:

- Baphomet NEVER makes a question to which he gave an answer the last time you met him.
- an unanswered question is just left there.
- an answered question gives up its place in the list to the unanswered one immediately below.

There are quicker ways to ask the questions. Each one of them is referred as a single word by the game. These are:

"Who was I?" -> "was"
"When did I die?" -> "when"
"Where did I die?" -> "where"
"Who killed me?" -> "killed"
"How did I get here?" -> "how"

Again, it does not matter if you ask Baphomet the whole questions or if you just type in the single words. Either one counts for a question made so just do as you please.

It does not matter how many tickets you have, if you kill / don't kill Jesus or if you die.

-- g-mecha gave me the fundamental idea, you can find his guide here
-- there's a dude on YouTube who allowed me to see what I was missing, his name on Steam is FingerRocks, you can see his video here
-- gemberling gave me some insights on which chew a little