vim-bash-completion is a small vim plugin that makes bash completion accessible within vim. It provides the bash#complete command that returns a list of all available completions for its single argument. To try it out, just type :echo bash#complete('ls -') to get all arguments for the ls command.
With the help of vim's functionality to use self-defined completion functions, we can define a :Make command that provides handy completions for make targets.
function MakeCommandCompletion(ArgLead, CmdLine, CursorPos)
let l:words = split(a:CmdLine)
let l:words[0] = 'make'
let l:command = join(l:words)
return bash#complete(l:command)
endfunction
:command -nargs=* -complete=customlist,MakeCommandCompletion Make make <args>