Tcl, 212 bytes

puts "[string map -nocase {President Gwanjang\ nim Founder Gwanjang\ nim Master\ instructor Sabeom\ nim Teacher Gyosa\ nim Black\ Belt Dan Student Geup Color\ Belt Geup Master\ level Godanja} $argv], *side kick*"

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PHP, 241 bytes

<?=preg_replace(["#\b(President|Founder)\b#i","#\bMaster instructor\b#i","#\bTeacher\b#i","#\bBlack Belt\b#i","#\b(Studen|Color Bel)t\b#i","#\bMaster level\b#i"],[Gwanjang.$n=" nim",Sabeom.$n,Gyosa.$n,Dan,Geup,Godanja],"$argn, *side-kick*");

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Retina, 154 bytes

i(`president|founder
Gwanjang_
master instructor
Sabeom_
teacher
Gyosa_
black belt
Dan
student|color belt
Geup
master level
Godanja
_
 nim
$
, *side kick*

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Retina, 163 bytes

i`President|Founder
Gwanjang¶
i`Master instructor
Sabeom¶
i`Teacher
Gyosa¶
i`Black Belt
Dan
i`Student|Color Belt
Geup
i`Master level
Godanja
¶
 nim
$
, *side kick*

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JavaScript (ES6), 233 bytes

s=>(btoa`>·¬×§·mÁ©ãjx4)µ§uêö§©àÒx¦ÔƬµêô{-®ç-¢½i·¨IâTÞiÈ^¯a²¢Æ´)µV@^Ýj}R¶ç^Ýzêu
h¯@^Ýzêu1«-z½%z÷¥ØjjxÚ`.split(0).join` `.split`1`.map(d=>([a,b]=d.split(/2+/),s=s.replace(RegExp(a,'gi'),b))),s+', *side kick*"')

f=
s=>(btoa`>·¬‰×§·m†Á©ãjx4ž)µ‹§uêö§©àÒx¦ÔƬµêôŠ{-®ç-¢½’i·¨›Iâ›TÞiÈ^¯a²¢Æ´ž)µVœ“@^–݃j}R¶ç^žÝ†zêu
‰h¯@^–݆zêu1«-z½%z÷¥ØjjxÚ`.split(0).join` `.split`1`.map(d=>([a,b]=d.split(/2+/),s=s.replace(RegExp(a,'gi'),b))),s+', *side kick*"')

console.log(f('I am a Teacher willing to be a President'))

JavaScript (ES6), 243 bytes

s=>(`President${A=':Gwanjang nim|'}Founder${A}Master instructor:Sabeom nim|Teacher:Gyosa nim|Black Belt:Dan|Student:Geup|Color Belt:Geup|Master level:Godanja`.split`|`.map(r=>([a,b]=r.split`:`,s=s.replace(RegExp(a,'gi'),b))),s+', *side kick*')

f=
s=>(`President${A=':Gwanjang nim|'}Founder${A}Master instructor:Sabeom nim|Teacher:Gyosa nim|Black Belt:Dan|Student:Geup|Color Belt:Geup|Master level:Godanja`.split`|`.map(r=>([a,b]=r.split`:`,s=s.replace(RegExp(a,'gi'),b))),s+', *side kick*')

console.log(f('I am a Teacher willing to be a President'))

JavaScript (ES6), 251 bytes

a=>a.replace(RegExp(b='president|founder|master instructor|teacher|black belt|student|color belt|master level','gi'),c=>((d='Gwanjang nim|')+d+'Sabeom nim|Gyosa nim|Dan|Geup|Geup|Godanja').split`|`[b.split`|`.indexOf(c.toLowerCase())])+', *side kick*'

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This is not as compact as it could be since JavaScript is so verbose, but it's a great question. I recognized most of these terms as I am a 2nd Dan Black Belt in Taekwondo.

Explanaion

a=>
  a.replace(                                    // Replace on input string
    RegExp(                                     // Regex matching English phrases
      b='president|founder|master instructor|teacher|black belt|student|color belt|master level',
      'gi'                                      // Match all, case insensitive
    ),
    c=>
      ((d='Gwanjang nim|')+d+                   // Duplicate string portion
        'Sabeom nim|Gyosa nim|Dan|Geup|Geup|Godanja') // Add remaining phrases
      .split`|`                                 // Split into array by pipe
        [b.split`|`.indexOf(c.toLowerCase())])  // Access Korean phrase by corresponding index of matched English phrase
      +', *side kick*'                          // I like to do side kicks

Python 3, 281 bytes

import re
x=input();a="Gwanjang";b=" nim";c="Geup";d="Master";e=" Belt"
for i in range(8):x=re.sub("(?i)"+["President","Founder",d+" instructor","Teacher","Black"+e,"Student","Color"+e,d+" level"][i],[a+b,a+b,"Sabeom"+b,"Gyosa"+b,"Dan",c,c,"Godanja"][i],x)
print(x+", *side kick*")

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C#, 262 bytes

s=>{for(int i=0;i<8;)s=s.ToUpper().Replace("PRESIDENT|FOUNDER|MASTER INSTRUCTOR|TEACHER|BLACK BELT|MASTER LEVEL|STUDENT|COLOR BELT".Split('|')[i],(i<2?"GWANJANG":i>3?"GEUP":"SABEOM|GYOSA|DAN|GODANJA".Split('|')[i-2])+(i++<4?" NIM":""));return s+", *SIDE KICK*";}

Full/Formatted version:

class Program
{
    static void Main(string[] args)
    {
        System.Func<string, string> f = s =>
        {
            for (int i = 0; i < 8;)
                s = s.ToUpper().Replace("PRESIDENT|FOUNDER|MASTER INSTRUCTOR|TEACHER|BLACK BELT|MASTER LEVEL|STUDENT|COLOR BELT".Split('|')[i],
                                        (i < 2 ? "GWANJANG"
                                               : i > 3 ? "GEUP"
                                                       : "SABEOM|GYOSA|DAN|GODANJA".Split('|')[i-2])
                                        + (i++ < 4 ? " NIM" : ""));

            return s + ", *SIDE KICK*";
        };

        System.Console.WriteLine(f("I am a Student and I do Taekwondo twice a week"));
        System.Console.WriteLine(f("I am a Teacher willing to be a President"));

        System.Console.ReadLine();
    }
}