Rise of the Tomb Raider Expedition Modes

Expeditions are additional modes of gameplay in Rise of the Tomb Raider. Each mode allows you to play Expedition Cards to modify your experience, and complete challenges for credits, which can be then used to acquire additional cards. In the standard edition the Expeditions you are able to play include Chapter Replay, Chapter Replay Elite, Score Attack, and Remnant Resistance.

Score Attack

Score Attack adds an arcade-inspired twist to Rise of the Tomb Raider. In Score Attack, you play through the chapters of campaign attempting to get the highest score you can.

The following give you points in Score Attack:

Score Attack Wisps and Lanterns: Throughout the level the player will find blue wisps and orange lanterns. Wisps are collected for points by touching them, while the lanterns must be shot. The farther away from a lantern you are when you shoot it, the more points its worth.
Kills: Players are granted points for every kill. The bigger the enemy, the more points you get. Additionally, certain types of kills may be worth more than a straight kill. Headshots, melee kills, and kills using crafted weapons are worth more than whittling an enemy down in direct confrontation. Additionally, the base value of an enemy kill is multiplied by the difficulty setting.
Pick Up Items: Any resource you harvest, chest you open, or ammo you find will give you points.
Combo Meter: Anything that gives you points increases your combo meter. The higher your combo meter, the more points you'll get from kills, items, wisps and lanterns. The combo meter will run out if you do not score points quickly enough, and will reset instantly if you take damage.
Damage, Death and Checkpoint Reloads: Every time you take damage, you lose points and reset your combo meter. Dying or reloading checkpoints resets your score to your last saved checkpoint, resets your meter, and subtracts an additional penalty. These penalties are bigger at higher difficulty settings.
Time: From the start of a Score Attack, a time bonus starts ticking down. The remainder left when you complete the chapter is added to your score.
Expedition Cards: The sum of your score plus time bonus is multiplied by the total bonus provided by cards you applied to your Score Attack session. Generally, this means that if you use a bunch of cards that make the game easier, your final Score Attack score will be less than if you used cards that made the game more challenging.

Once your final score is determined, you gain medals based on how close you were to the score "pars" for the mission. A gold medal means more credits than a silver, and a silver means more credits than a bronze.

You can look at Score Attack leaderboards and see how your friends or the community have scored per chapter. You can bring up the details of a player's performance, including their kills, deaths, and what cards they used. If you think you can do better than they did, you can challenge their score, which costs a small value of credits per card the player used. This way you can challenge your friends' scores, even if you don't have the cards they used.

Chapter Replay & Chapter Replay Elite

The Chapter Replay modes allow you to select and replay parts of Rise of the Tomb Raider's campaign. In Chapter Replay, you start the chapter with pre-determined inventory and skills. In Chapter Replay Elite, you start with the gear in your latest profile data from the campaign.

Remnant Resistance

Remnant Resistance is an objective-based challenge mode that is played in Rise's large "hub" spaces. You can choose to play existing Remnant Resistance missions made by your friends and the Tomb Raider community, or create your own mission. A Remnant Resistance mission is composed of 5 objectives, which can involve things like taking down a high value target, collecting intel documents, hunting animals, and more. Additionally, as the creator you can set Lara up with the costume and weapons of your choice, as well as apply up to five of the standard expedition cards as well. Lastly, you can choose where the challenge takes place, at what time, and what weather is active.

The harder the mission, the higher the reward (in credits). However, you must beat your own mission for it to be posted to the leaderboards. Difficulty can vary from objective to objective. For example, a normal difficulty objective to rescue hostages, followed by a high difficulty objective to take down a bear. Players familiar with Hitman: Absolution's Contracts Mode should feel right at home in Remnant Resistance.

When a creator posts their Remnant Resistance challenge, their friends are able to play it. When you play someone else's Remnant Resistance challenge, your score on their challenge is tracked, with the top 3 players being posted on the challenge. A week after the challenge was posted, the player with the highest score in that challenge is awarded credits and the challenge is removed.

Expedition Cards

In Rise of the Tomb Raider, you'll earn credits by completing challenges and exploring the world. These credits can be used to purchase Expedition Card packs. When used, Expedition Cards become modifiers in the extra game modes detailed above. Some cards are humorous, such as Big Head Mode, while others can increase the challenge or give you special advantages. There are two types of Expedition Cards: Foil and Common. Foil Cards offer the strongest or strangest variations and can be used as many times as you wish. A Common Card can only be used once, and you'll need to earn more credits to buy it back. Expedition Cards offer hundreds of ways to customize your Rise of the Tomb Raider experience. Uncover, unlock, experiment, and enjoy!

The majority of cards are consumed once you've completed a mode. If you've created a Score Attack mission that is too difficult to complete and choose to quit, you won't lose your cards.

You can get cards in several ways:

Playing the campaign: As you make your way through the campaign's story you'll receive card packs after you complete certain chapters.
Playing Expedition modes: As you reach milestones of challenges completed, Remnant Resistance missions completed, and Score Attack medals collected, you are gifted additional cards.
Spending credits: Credits earned from Expedition modes are meant for purchasing additional cards. Credits can be used to buy any of the card packs in the market.
Real money: For those of us that want those cards and want them now, most card packs can also be purchased with real world money.

The "base" card packs:

Bronze Pack: Five cards chosen at random. Only purchasable with credits.
Silver Pack: Five cards chosen at random, one of which is guaranteed to be of 'Uncommon' rarity. Can be purchased with either credits or real money.
Gold Pack: Five cards chosen at random, one of which is guaranteed to be of 'Rare' rarity. Can be purchased with either credits or real money.
Advantage Pack: Five cards chosen at random that give the player an edge. Purchasable with credits or money.
Challenge Pack: Five cards chosen at random that increase the difficulty for the player. Purchasable with credits or real money.
Wild Pack: Five cards chosen at random from the cards with the strangest effects. Purchasable with credits or real money.

Credits

There are many ways for you to earn credits to use in Rise of the Tomb Raider’s Expeditions:

Playing the campaign: Various activities such as challenges, finding relics, and story progression will gift players with additional credits.
Challenge Tombs: Completing challenge tombs while playing the campaign will earn you additional credits.
Expedition Challenges: In Chapter Replay, Chapter Replay Elite, and Score Attack, you can select up to five challenges to attempt when selecting a chapter to play. Completing challenges results in a credit reward, the value of which is determined by the difficulty of the challenge.
Score Attack: As previously mentioned, if you score high enough in a game of Score Attack to earn a medal, you will earn credits based on which medal you earn.
Remnant Resistance: Playing and completing missions will earn you credits both for completing objectives and for entire missions.
Sell Cards: While creating a mission, you are able to sell your unnecessary cards.

There are additional ways to earn credits in Rise of the Tomb Raider, ensuring you always have enough cards to experiment and challenge your friends in Expeditions.

Challenges

Challenges are an additional method of earning credits available to people playing Chapter Replay, Chapter Replay Elite, and Score Attack. Each chapter has a selection of challenges that can be selected, and the player can go into a session with up to five challenges active. Completing a challenge nets the player credits, with the amount of credits earned depending on the difficulty of the challenge.

Once a challenge is completed, a short period is required before a challenge can be repeated. If a challenge is failed, the challenge will remain available for another attempt and can even be attempted by restarting the chapter from the pause menu.

Source: official Rise of the Tomb Raider FAQs
Screenshots: Raiding The Globe