You can get all the data in json format, ll you need to do is parse a value from script tag inside the original page source and pass it to "http://www.lolking.net/leaderboards/some_value_here/eune/1.json":
from bs4 import BeautifulSoup
import requests
import re
patt = re.compile("\$\.get\('/leaderboards/(\w+)/")
js = "http://www.lolking.net/leaderboards/{}/eune/1.json"
soup = BeautifulSoup(requests.get("http://www.lolking.net/leaderboards#/eune/1").content)
script = soup.find("script", text=re.compile("\$\.get\('/leaderboards/"))
val = patt.search(script.text).group(1)
data = requests.get(js.format(val)).json()
data gives you json that contains all the player info like:
{'data': [{'division': '1',
'global_ranking': '12',
'league_points': '1217',
'lks': '2961',
'losses': '31',
'most_played_champions': [{'assists': '238',
'champion_id': '236',
'creep_score': '7227',
'deaths': '131',
'kills': '288',
'losses': '5',
'played': '39',
'wins': '34'},
{'assists': '209',
'champion_id': '429',
'creep_score': '5454',
'deaths': '111',
'kills': '204',
'losses': '3',
'played': '27',
'wins': '24'},
{'assists': '155',
'champion_id': '81',
'creep_score': '4800',
'deaths': '103',
'kills': '168',
'losses': '8',
'played': '26',
'wins': '18'}],
'name': 'Sadastyczny',
'previous_ranking': '2',
'profile_icon_id': 7,
'ranking': '1',
'region': 'eune',
'summoner_id': '42893043',
'tier': '6',
'tier_name': 'CHALLENGER',
'wins': '128'},
{'division': '1',
'global_ranking': '30',
'league_points': '1128',
'lks': '2956',
'losses': '180',
'most_played_champions': [{'assists': '928',
'champion_id': '24',
'creep_score': '37601',
'deaths': '1426',
'kills': '1874',
'losses': '64',
'played': '210',
'wins': '146'},
{'assists': '501',
'champion_id': '67',
'creep_score': '16836',
'deaths': '584',
'kills': '662',
'losses': '37',
'played': '90',
'wins': '53'},
{'assists': '124',
'champion_id': '157',
'creep_score': '5058',
'deaths': '205',
'kills': '141',
'losses': '14',
'played': '28',
'wins': '14'}],
'name': 'Richor',
'previous_ranking': '1',
'profile_icon_id': 577,
'ranking': '2',
'region': 'eune',
'summoner_id': '40385818',
'tier': '6',
'tier_name': 'CHALLENGER',
'wins': '254'},
{'division': '1',
'global_ranking': '49',
'league_points': '1051',
'lks': '2953',
'losses': '47',
'most_played_champions': [{'assists': '638',
'champion_id': '117',
'creep_score': '11927',
'deaths': '99',
'kills': '199',
'losses': '7',
'played': '66',
'wins': '59'},
{'assists': '345',
'champion_id': '48',
'creep_score': '8061',
'deaths': '99',
'kills': '192',
'losses': '11',
'played': '43',
'wins': '32'},
{'assists': '161',
'champion_id': '114',
'creep_score': '5584',
'deaths': '64',
'kills': '165',
'losses': '11',
'played': '31',
'wins': '20'}],