Non-competitive TrophiesThese are that do NOT require you to compete against actual players either directly or indirectly.
Beating Punchbag Bob: A pet of any level can beat Punchbag Bob in the battledome, but it will take longer if your pet is weak and has cheap weapons. Depending on your stamina level for sitting and clicking the same thing over and over again you can go for it without much of a battledome set or train your pet and get good weapons before going for this trophy.
Cellblock: This game is a Neopets version of Connect Four, except you need five to win against the computer. This game requires strategy and a lot of time to get gold, but once you find a strategy that works you will have gold in no time. You receive a medal for your lookup after completing Level 4 of Tournament 1. The medal is upgraded to a bronze trophy at Level 8 of Tournament 1, a silver trophy after Level 4 of Tournament 11, and a gold trophy after Level 8 of Tournament 11.
Cheat!: This is Neopets version of the BS card game. This game is not just good for earning an easy trophy, but you can earn neopoints and battle cards. In each round you face three computer opponents. After beating Round 3 you will get a bronze trophy. The trophy is upgraded to silver after Round 5 and gold after Round 7.
Defenders of Neopia: In this game you are given a mission to defeat a certain one-player battledome character. The characters get harder as you go, but after you beat each character your trophy on your lookup is upgraded to show how far you have gotten in the series. There are two series of missions. You do not have to finish series one to start series two, nor does your pet have to be stronger to start series two than to start series one, as both series start out with relatively easy opponents.
Go! Go! Go!: This is a Neopets card game played against three computer players. I am not sure what real life card game it is like or if it even resembles one. I find this to be one of the hardest card games on Neopets. Be sure to read the rules before you start playing. It may take a few rounds to get a hang of the game. You receive a bronze trophy after beating Round 2. It is upgraded to silver after Round 6 and gold after Round 8.
Invasion of Meridell: This is a strategy game played against the computer in Meridell. This game is relatively easy at the beginning, especially if you can master a strategy, but it gets harder as you go requiring a more refined strategy. You get a runner up medal if you beat Mission 5.
Neoquest: This is a role playing adventure game that takes a lot of time to beat, but if you put some time into every day and find a good guide to it you can beat it. You do not lose you progress unless you deliberately start over. You get a bronze trophy for winning on normal difficulty, a silver trophy for winning on evil difficulty, and a gold trophy for winning on insane difficulty. You must beat the difficulty levels in order.
Neoquest II: Longer sequel to Neoquest. It takes even more commitment, but attainable if you put the effort into it. Bronze awarded after Normal difficulty finished, silver after evil difficulty finished, and gold after insane difficulty finished. As in Neoquest you must beat the difficulty levels in order.
Pyramid Bonus: This card game is found in the Lost Desert. You can get a bronze trophy by clearing the pyramid twice (does not have to be in a row). The trophy is upgraded to silver if you win four times. The gold upgrade is hard to get, as you need to win twice in a row, but if you have the patience to come back and play to your max of 5,000 NP in winnings everyday you efforts will eventually be rewarded.
Round Table Poker: This is Neopets version of poker played against three computer players. This game takes strategy, luck, and time. You get a runner up medal after beating Round 5. Sakhmet
Solitaire Bonus: This is Neopets version of traditional Solitaire. You can get a bronze trophy by winning twice (does not have to be in a row). The trophy is upgraded to silver if you win four times. The gold upgrade is hard to get, as you need to win twice in a row, but if you have the patience to come back and play to your max of 5,000 NP in winnings everyday you efforts will eventually be rewarded.
Snow Wars: This is Neopets version of battleship. You play against different computer players. It cost 100 NP per round. Each time you win you get some snowballs, which get better the further you get. There are a total of 10 rounds. You receive a medal for your lookup once you beat Round 2. The medal is upgraded to a bronze trophy after Round 4, a silver trophy after Round 7, and a gold trophy after Round 10.