Lots of DRY code. I tried to avoid it but it would not work, so I used DRY code to make it work.

var student = [
  {name: "Susan", track: "Web Design", achievements: 2, points: 25},
  {name: "Melissa", track: "Full Stack Dev", achievements: 3, points: 50},
  {name: "Sarah", track: "Front End Dev", achievements: 4, points: 75},
  {name: "Jennifer", track: "IOS",achievements: 5, points: 100},
  {name: "Alexia", track: "Python", achievements: 6, points: 125}
];

function print(x) {
  document.getElementById('output').innerHTML = x;
}

while (true) {
  var userInput = prompt("Enter student name. Type 'quit' to exit");
  userInput = userInput.toLowerCase();
  if (userInput === "alexia") {
    alexia();
  } else if (userInput === "susan") {
    susan();
  } else if (userInput === "melissa") {
    melissa();
  } else if (userInput === "jennifer") {
    jennifer();
  } else if (userInput === "sarah") {
    sarah();
  } else if (userInput === "quit") {
    break;
  }
}

function susan() {
  for (var i = 0; i = 5; i++) {
  var message = '';
      message = message + '<h3>' + 'Student name: ' + student[0].name + '</h3>';
      message = message + '<p>' + 'Track: ' + student[0].track + '</p>';
      message = message + '<p>' + 'Acheivments: ' + student[0].achievements + '</p>';
      message = message + '<p>' + 'Points: ' + student[0].points + '</p>';
  print(message);
  break;
  }
}

function melissa() {
  for (var i = 0; i = 5; i++) {
  var message = '';
      message = message + '<h3>' + 'Student name: ' + student[1].name + '</h3>';
      message = message + '<p>' + 'Track: ' + student[1].track + '</p>';
      message = message + '<p>' + 'Acheivments: ' + student[1].achievements + '</p>';
      message = message + '<p>' + 'Points: ' + student[1].points + '</p>';
  print(message);
  break;
  }
}

function sarah() {
  for (var i = 0; i = 5; i++) {
  var message = '';
      message = message + '<h3>' + 'Student name: ' + student[2].name + '</h3>';
      message = message + '<p>' + 'Track: ' + student[2].track + '</p>';
      message = message + '<p>' + 'Acheivments: ' + student[2].achievements + '</p>';
      message = message + '<p>' + 'Points: ' + student[2].points + '</p>';
  print(message);
  break;
  }
}

function jennifer() {
  for (var i = 0; i = 5; i++) {
  var message = '';
      message = message + '<h3>' + 'Student name: ' + student[3].name + '</h3>';
      message = message + '<p>' + 'Track: ' + student[3].track + '</p>';
      message = message + '<p>' + 'Acheivments: ' + student[3].achievements + '</p>';
      message = message + '<p>' + 'Points: ' + student[3].points + '</p>';
  print(message);
  break;
  }
}

function alexia() {
  for (var i = 0; i = 5; i++) {
  var message = '';
      message = message + '<h3>' + 'Student name: ' + student[4].name + '</h3>';
      message = message + '<p>' + 'Track: ' + student[4].track + '</p>';
      message = message + '<p>' + 'Acheivments: ' + student[4].achievements + '</p>';
      message = message + '<p>' + 'Points: ' + student[4].points + '</p>';
  print(message);
  break;
  }
}