Mew is unique in both its method of encounter and its method of capture.
Mew can only be encountered if the following conditions are met:
If all of these conditions are true, Mew will have a 6.25% chance of being the Pokémon chosen to catch once Catch 'em Mode is initiated. When Mew is a potential encounter, it drops Mewtwo's encounter rate from 18.75% to 12.5%.
Encountering Mew will cause the Mewtwo bonus counter to reset to 0, so if the player wants to encounter Mew a second time in the same run, they will need to first beat the Mewtwo bonus twice.
To access Indigo Plateau, the player must move to a new map 5 times on a single run; the 5th move will take the player to Indigo Plateau. If the player moves again from Indigo Plateau, they will have to move to a new map another 5 times to reach Indigo Plateau a second time.
Each bonus requires three Poké Ball icons on the field, or for the player to play the slots and land on the Go to Bonus option (see Slots for the slot sets). One Poké Ball icon is obtained for every Pokémon caught, and two for every Pokémon evolved. The player must beat each bonus stage to move on to the next. Thus, the player will need to obtain at minimum 9 Poké Ball icons to get the Mewtwo bonus the first time, and at minimum 9 to get the Mewtwo bonus the second time, for a total of a minimum of 18 Poké Ball icons (this ignores the probability of going to a bonus via the slots).
When starting Catch 'em Mode, the Rare table will be selected if all three lights on the right loop are lit. If the player starts Catch 'em Mode through the slots, the game has a 50% chance of choosing the Rare table to take its Pokémon from.
All other Pokémon in the game can be captured by hitting the bumpers six times to flip the Pokémon icon, and then hitting the Pokémon four times to catch it. However, in the case of Mew, the game actually requires the player to hit it 1,024 times in order to catch it. This is of course impossible for any player playing without tool assistance, so it is impossible to actually hit Mew enough times to make it go into the Poké Ball. Instead, Mew's Pokédex entry will be unlocked by encountering it rather than capturing it. Hitting it instead just gives the player points.