Every time I run Battlespire I get this huge black border. When I run Arena and Daggerfall (Installed from the Elder Scrolls Anthology) they go full screen perfectly fine. How do I make Battlespire fit the screen?

Sometimes there's a setting on your monitor. Try alt+enter too.

That looks to me like misconfigured DOSBox. Can you post the contents of the .conf file(s) in the Battlespire folder? I should be able to tell you if anything looks amiss.

# This is the configuration file for DOSBox 0.74-2. (Please use the latest version of DOSBox)
# Lines starting with a # are comment lines and are ignored by DOSBox.
# They are used to (briefly) document the effect of each option.

[sdl]
# fullscreen: Start dosbox directly in fullscreen. (Press ALT-Enter to go back)
# fulldouble: Use double buffering in fullscreen. It can reduce screen flickering, but it can also result in a slow DOSBox.
# fullresolution: What resolution to use for fullscreen: original, desktop or fixed size (e.g. 1024x768).
# Using your monitor's native resolution (desktop) with aspect=true might give the best results.
# If you end up with small window on a large screen, try an output different from surface.
# On Windows 10 with display scaling (Scale and layout) set to a value above 100%, it is recommended
# to use a lower full/windowresolution, in order to avoid window size problems.
# windowresolution: Scale the window to this size IF the output device supports hardware scaling.
# (output=surface does not!)
# output: What video system to use for output.
# Possible values: surface, overlay, opengl, openglnb, ddraw.
# autolock: Mouse will automatically lock, if you click on the screen. (Press CTRL-F10 to unlock)
# sensitivity: Mouse sensitivity.
# waitonerror: Wait before closing the console if dosbox has an error.
# priority: Priority levels for dosbox. Second entry behind the comma is for when dosbox is not focused/minimized.
# pause is only valid for the second entry.
# Possible values: lowest, lower, normal, higher, highest, pause.
# mapperfile: File used to load/save the key/event mappings from. Resetmapper only works with the defaul value.
# usescancodes: Avoid usage of symkeys, might not work on all operating systems.

fullscreen=true
fulldouble=false
fullresolution=desktop
windowresolution=original
output=overlay
autolock=true
sensitivity=100
waitonerror=true
priority=higher,normal
mapperfile=mapper-0.74-2.map
usescancodes=true

I only posted down to what looks like where the screen would be, otherwise it seems the website won't post the whole thing. Taking forever to process. Let me know if I need to post any more than that

Should be changed to "original", which should fix your issue.

Or just try specifying your desired resolution here.

EDIT:
Never mind. That will most likely just change the size of the window itself and not increase the game area. So yeah, do what Mr.Mumbles suggested.

And there are even these notes in the file:
# Using your monitor's native resolution (desktop) with aspect=true might give the best results.
# If you end up with small window on a large screen, try an output different from surface.

# This is the configuration file for DOSBox 0.74-2. (Please use the latest version of DOSBox)
# Lines starting with a # are comment lines and are ignored by DOSBox.
# They are used to (briefly) document the effect of each option.

[sdl]
# fullscreen: Start dosbox directly in fullscreen. (Press ALT-Enter to go back)
# fulldouble: Use double buffering in fullscreen. It can reduce screen flickering, but it can also result in a slow DOSBox.
# fullresolution: What resolution to use for fullscreen: original, desktop or fixed size (e.g. 1024x768).
# Using your monitor's native resolution (desktop) with aspect=true might give the best results.
# If you end up with small window on a large screen, try an output different from surface.
# On Windows 10 with display scaling (Scale and layout) set to a value above 100%, it is recommended
# to use a lower full/windowresolution, in order to avoid window size problems.
# windowresolution: Scale the window to this size IF the output device supports hardware scaling.
# (output=surface does not!)
# output: What video system to use for output.
# Possible values: surface, overlay, opengl, openglnb, ddraw.
# autolock: Mouse will automatically lock, if you click on the screen. (Press CTRL-F10 to unlock)
# sensitivity: Mouse sensitivity.
# waitonerror: Wait before closing the console if dosbox has an error.
# priority: Priority levels for dosbox. Second entry behind the comma is for when dosbox is not focused/minimized.
# pause is only valid for the second entry.
# Possible values: lowest, lower, normal, higher, highest, pause.
# mapperfile: File used to load/save the key/event mappings from. Resetmapper only works with the defaul value.
# usescancodes: Avoid usage of symkeys, might not work on all operating systems.

fullscreen=true
fulldouble=false
fullresolution=original
windowresolution=original
output=openglnb
autolock=true
sensitivity=100
waitonerror=true
priority=higher,normal
mapperfile=mapper-0.74-2.map
usescancodes=true
___________________________________________________________________________________________
Try this one!

Note: Surface does not support scaling or aspect correction.

Openglnb = Opengl No Bilinear filtering

That's not a good solution, it just forces the monitor to use a display mode it doesn't necessarily support properly.

I'll give them all a shot and see what happens. I'll probably also check what Arena and Daggerfall are set to since they work perfectly fine

SirPrimalform's settings did exactly what I wanted it to

Glad I could help!