HTML （Swiper sample 06 と同じ）

<div class="swiper-container">
  <div class="swiper-wrapper">
    <div class="swiper-slide">
      <div class="slide-img posChg1" style="background-image: url('images/swiper_img_01.jpg')"></div>
      <div class="slide-content">
        <h1 class="from_top">Slide Title 01</h1>
        <p>Lorem ipsum dolor sit amet, consectetur</p>
        <div class="caption">caption 01</div>
      </div>
    </div>
    <div class="swiper-slide">
      <div class="slide-img posChg2" style="background-image: url('images/swiper_img_02.jpg')"></div>
      <div class="slide-content">
        <h2 class="from_left">Slide Title 02</h2>
        <p class="from_right">Ipsa, quis ex repudiandae eum </p>
        <div class="caption">caption 02</div>
      </div>
    </div>
    <div class="swiper-slide">
      <div class="slide-img posChg3" style="background-image: url('images/swiper_img_03.jpg')"></div>
      <div class="slide-content">
        <h3 class="from_bottom">Slide Title 03</h3>
        <p>Ullam rerum quasi libero esse </p>
        <div class="caption">caption 03</div>
      </div>
    </div>
  </div><!-- end of .swiper-wrapper -->
  <div class="swiper-pagination swiper-pagination-white"></div>
  <div class="swiper-button-prev"></div>
  <div class="swiper-button-next"></div>
</div><!-- end of .swiper-container -->

CSS（Swiper sample 06との違いは高さの値とアニメーション部分のみ）

/* 変更部分 */
.swiper-container{
  max-width: 720px; 
}
.slide-img { 
  /* 表示される領域（スライダー）の高さが画像の高さより小さくなるように調整 */
  height: 360px;   
  background-size: cover;
  background-position: center center;
  background-repeat: no-repeat;
  overflow:visible;
}

/* 垂直方向のアニメーション background-position の2つ目のパラメータで指定 */
@keyframes posChg1 {
  0% {
    background-position: center top;
    /*background-position: center 0%; と同じ*/ 
  }
  100% {
    background-position: center center;
  }
}
.swiper-slide-active .posChg1 {
  animation: posChg1 4s linear 0s 1 normal both;
} 
@keyframes posChg2 {
  0% {
    background-position: center 70%;
  }
  100% {
    background-position: center 30%;
  }
}
.swiper-slide-active .posChg2 {
  animation: posChg2 6s linear 0s 1 normal both;
} 
@keyframes posChg3 {
  0% {
    background-position: center center;
  }
  100% {
    background-position: center 100%;
    /*background-position: center bottom; と同じ*/
  }
}
.swiper-slide-active .posChg3 {
  animation: posChg3 2s linear 0s 1 normal both;
} 

/* 変更部分 ここまで */


.swiper-slide .slide-content h1, .swiper-slide .slide-content h2, .swiper-slide .slide-content h3 {
  position: absolute;
  top: 20%;
  left: 50%;
  transform: translate(-50%, -50%);
  color: #FFF;
  font-size: 30px;
  text-shadow: 2px 2px rgba(0,0,0,0.3);
}
.swiper-slide .slide-content p {
  position: absolute;
  top: 50%;
  left: 50%;
  transform: translate(-50%, -50%);
  color: #FFF;
  text-shadow: .5px .5px rgba(0,0,0,0.6);
  margin: 0;
  padding: 0;
  font-size: 18px;
}
.swiper-slide .slide-content .caption {
  position: absolute;
  bottom: 30px;
  right: 30px;
  color: #FFF;
  font-size: 16px;
  background-color: rgba(0,127,127,0.5);
  padding: 3px 8px;
}

/* 文字のアニメーション */

@keyframes fromTop {
  0% {
    top: 0%;
    opacity: 0;
  }
  100% {
    top: 20%;
    opacity: 1;
  }
}  
  
@keyframes fromBottom {
  0% {
    top: 80%;
    opacity: 0;
  }
  100% {
    top: 20%;
    opacity: 1;
  }
}  

@keyframes fromleft {
  0% {
    left: 0%;
    opacity: 0;
  }
  100% {
    left: 50%;
    opacity: 1;
  }
}
  
@keyframes fromRight {
  0% {
    left: 100%;
    opacity: 0;
  }
  100% {
    left: 50%;
    opacity: 1;
  }
}
 
/* .from_top を指定した要素のアニメーション */
.swiper-slide-active .from_top {
  animation: fromTop .6s ease-in-out 0s 1 normal both;
} 
  
/* .from_bottom を指定した要素のアニメーション */
.swiper-slide-active .from_bottom {
  animation: fromBottom .6s ease-in-out 0s 1 normal both;
} 
  
/* .from_left を指定した要素のアニメーション */
.swiper-slide-active .from_left {
  animation: fromleft .6s ease-in-out 0s 1 normal both;
} 
  
/* .from_right を指定した要素のアニメーション */
.swiper-slide-active .from_right{
  animation: fromRight .6s ease-in-out .5s 1 normal both;
}

JavaScript

<script>
  let mySwiper = new Swiper ('.swiper-container', {
    loop: true,
    
    pagination: {
      el: '.swiper-pagination',
      clickable: true,
    },

    navigation: {
      nextEl: '.swiper-button-next',
      prevEl: '.swiper-button-prev',
    },

  })
</script>