Достать самое большое значение из JSON php

Можете попробовать так։

        $json = json_decode('{"type":"message_new","object":{"date":1543246468,"from_id":515828454,"id":133013,"out":0,"peer_id":515828454,"text":"","conversation_message_id":2361,"fwd_messages":[],"important":false,"random_id":0,"attachments":[{"type":"photo","photo":{"id":456239327,"album_id":-15,"owner_id":515828454,"sizes":[{"type":"m","url":"https:\/\/sun9-6.userapi.com\/c540100\/v540100328\/6fa71\/dHtVkQA6VWY.jpg","width":118,"height":130},{"type":"o","url":"https:\/\/sun9-5.userapi.com\/c540100\/v540100328\/6fa73\/UK6ebeydZ14.jpg","width":130,"height":144},{"type":"p","url":"https:\/\/sun9-1.userapi.com\/c540100\/v540100328\/6fa74\/Dw2Lmcufbrc.jpg","width":200,"height":221},{"type":"q","url":"https:\/\/sun9-6.userapi.com\/c540100\/v540100328\/6fa75\/MoDZzCcBkrQ.jpg","width":320,"height":353},{"type":"r","url":"https:\/\/sun9-3.userapi.com\/c540100\/v540100328\/6fa76\/fVo81F2GeeI.jpg","width":480,"height":530},{"type":"s","url":"https:\/\/sun9-4.userapi.com\/c540100\/v540100328\/6fa70\/2eBzwe4T8kc.jpg","width":68,"height":75},{"type":"x","url":"https:\/\/sun9-4.userapi.com\/c540100\/v540100328\/6fa72\/1_V4Eu_MF7w.jpg","width":480,"height":530}],"text":"","date":1542804864,"access_key":"74b9f9163c1a2f93ac"}}],"is_hidden":false},"group_id":173657849}');
        $image = $json->object->attachments[0]->photo->sizes;
        $key = array_keys($image, max($image))[0];
        $bigImage = $image[$key]->url;
    print_r($bigImage);
 /*
    Самый большой формат
    https://sun9-4.userapi.com/c540100/v540100328/6fa72/1_V4Eu_MF7w.jpg
*/

На самом деле там как понимаю "type": "m" и т.п. означают размеры и можно брать не вычислениями, а по типу. Курите мануал, предполагаю что "type": "x" (XL) это самая большая.

Но предложу и свой вариант кода с сортировкой (мне кажется он правильнее чем у @Arsen):

$json = json_decode('{"type":"message_new","object":{"date":1543246468,"from_id":515828454,"id":133013,"out":0,"peer_id":515828454,"text":"","conversation_message_id":2361,"fwd_messages":[],"important":false,"random_id":0,"attachments":[{"type":"photo","photo":{"id":456239327,"album_id":-15,"owner_id":515828454,"sizes":[{"type":"m","url":"https:\/\/sun9-6.userapi.com\/c540100\/v540100328\/6fa71\/dHtVkQA6VWY.jpg","width":118,"height":130},{"type":"o","url":"https:\/\/sun9-5.userapi.com\/c540100\/v540100328\/6fa73\/UK6ebeydZ14.jpg","width":130,"height":144},{"type":"p","url":"https:\/\/sun9-1.userapi.com\/c540100\/v540100328\/6fa74\/Dw2Lmcufbrc.jpg","width":200,"height":221},{"type":"q","url":"https:\/\/sun9-6.userapi.com\/c540100\/v540100328\/6fa75\/MoDZzCcBkrQ.jpg","width":320,"height":353},{"type":"r","url":"https:\/\/sun9-3.userapi.com\/c540100\/v540100328\/6fa76\/fVo81F2GeeI.jpg","width":480,"height":530},{"type":"s","url":"https:\/\/sun9-4.userapi.com\/c540100\/v540100328\/6fa70\/2eBzwe4T8kc.jpg","width":68,"height":75},{"type":"x","url":"https:\/\/sun9-4.userapi.com\/c540100\/v540100328\/6fa72\/1_V4Eu_MF7w.jpg","width":480,"height":530}],"text":"","date":1542804864,"access_key":"74b9f9163c1a2f93ac"}}],"is_hidden":false},"group_id":173657849}',true);

    $image = $json['object']['attachments'][0]['photo']['sizes'];
    usort($image, function($a,$b){return ($b['width']-$a['width']);});
    $bigImage=$image[0]['url'];
    print_r($bigImage); die();