The keyboard support of Megaman X Legacy Collection has a number of limitations. The in-game option to rebind the controls resets every time the game is launched, and you can only bind to ASDFZXCV. Also, no options are available to remap the movement keys from the arrow keys, and the config.ini file does not allow you to configure the keyboard controls either.

To get around these limitations and bind the game's controls to whatever keys you want, other software is needed. Although other options exist, for this guide, we will be using Autohotkey, which is a safe, free, and efficient way to accomplish this.

EDIT 2: Thanks to a similar guide by Miagui here, I was able to fix the dropped inputs in X7 and X8 by adding some optimizations. I also found another fix in a thread about using autohotkey with games. Both are included in the sample autohotkey script below (altered to fit the conventions of autohotkey V2).

EDIT: Just as a note, I was able to finish X1-X4 with no hiccups using this method. From my testing so far, x5 and x6 work fine as well. However, in X7 and X8 only, there are issues with dropped inputs on the remapped keys, which make them unplayable using this method. I was unable to fix this with autohotkey, but I did find that another remapping tool called 'reWASD' worked with these games. Therefore, if you wish to play X7 or X8 with remapped keyboard controls, I recommend you use reWASD instead. Unlike autohotkey, which requires you to write a script, reWASD has a intuitive UI for remapping controls however you want, but the downside is that it is paid software. As of the time of writing, it has a free trial available, so you can easily try it out and pay for it later if it is worth it for you.

First, download and install Autohotkey from https://www.autohotkey.com/.

Go to the folder where Steam installed the game, for example: C:\Program Files (x86)\Steam\steamapps\common\Mega Man X Legacy Collection\.

Next, right click and select new -> AutoHotkey Script, then give it a name such as "keybindings", select the option "minimal for v2" if available, then click create. Alternatively, create a text file then give it the ".ahk" file extension instead.

Once the ahk file is created, open it with notepad or another text editor, then use autohotkey's syntax to create the mapping from the game's default keyboard controls to your desired controls line-by-line.

https://www.autohotkey.com/docs/v2/KeyList.htm
The basic syntax you'll want to use for each keybinding line is
For example, a line with will map the w key to the up arrow key.

For reference, here are the default keyboard controls for Megaman X1-X3, taken from the in-game option screen


To make sure that the bindings only take effect when the game is running, wrap the bindings between lines with and
The following line is also helpful to stop a warning message from popping up if you press too many of your bindings within the span of a couple of seconds.

Lines that start with ';' are comments that will be ignored by Autohotkey

Your file should end up resembling something like the following:

Here is a sample file, which binds movement to esdf, dash to left shift, jump to spacebar, and the other actions to the keypad. Additional Optimizations are included to make X7 and X8 playable. Feel free to use it as a template for your own bindings. Note that the 'rehook' line should only be uncommented as a last resort if x7 and x8 are still dropping inputs with these optimizations, because it will introduce another problem where you are unable to hold down your bindings for long.

Once the autohotkey file is made, run it by double clicking it or right clicking and selecting 'Open Script'. If the script is running successfully, you will be able to see it on the system tray

Now you are ready to launch the game and play using your own keyboard bindings.

The script needs to be running before launching the game, but it might be possible to automate this by having the script launch the game automatically using some autohotkey command (documentation is available at https://www.autohotkey.com/docs/v2/), compiling it into an exe file, and then launching the game from a shortcut of that exe instead of directly from steam.