Arch Archer is an achievement that requires the player to have the Competition Judge from the Ranging Guild competition congratulate the player for acquiring over 1,000 archery tickets.
Bring some coins for the entrance fee (200 coins per game). Players with a high Ranged level with good bonuses, may likely play about 40 games before obtaining 1,000 tickets so bring 6,000-10,000 coins to pay for the multiple tries it will take. Players with level 70+ Ranged with a magic bow should be able to complete it in less than 25 turns. Lower-level players may have to play closer to 100 games, so bring 20,000 coins. Alternatively, players can buy 1,000 tickets from the Grand Exchange for 17,000 coins.